diff --git a/src/__tests__/lib/exampleData.js b/src/__tests__/lib/exampleData.js
index abc22401009..675c3392cef 100644
--- a/src/__tests__/lib/exampleData.js
+++ b/src/__tests__/lib/exampleData.js
@@ -248,6 +248,7 @@ export const makeAccount = (
     zulipVersion: zulipVersionInner,
     ackedPushToken,
     lastDismissedServerPushSetupNotice,
+    silenceServerPushSetupWarnings: null,
   });
 };
 
@@ -648,6 +649,7 @@ export const plusReduxState: GlobalState & PerAccountState = reduxState({
       zulipVersion: recentZulipVersion,
       zulipFeatureLevel: recentZulipFeatureLevel,
       lastDismissedServerPushSetupNotice: null,
+      silenceServerPushSetupWarnings: false,
     },
   ],
   realm: {
diff --git a/src/account/AccountItem.js b/src/account/AccountItem.js
index f41cf378be1..26173a6d269 100644
--- a/src/account/AccountItem.js
+++ b/src/account/AccountItem.js
@@ -62,7 +62,8 @@ type Props = $ReadOnly<{|
 |}>;
 
 export default function AccountItem(props: Props): Node {
-  const { email, realm, isLoggedIn, notificationReport } = props.account;
+  const { email, realm, isLoggedIn, notificationReport, silenceServerPushSetupWarnings } =
+    props.account;
 
   const _ = React.useContext(TranslationContext);
   const navigation = useNavigation();
@@ -91,7 +92,10 @@ export default function AccountItem(props: Props): Node {
     isActiveAccount && activeAccountState != null && getHaveServerData(activeAccountState)
       ? getRealmName(activeAccountState)
       : '(unknown organization name)';
-  const singleNotifProblem = chooseNotifProblemForShortText({ report: notificationReport });
+  const singleNotifProblem = chooseNotifProblemForShortText({
+    report: notificationReport,
+    ignoreServerHasNotEnabled: silenceServerPushSetupWarnings ?? false,
+  });
 
   const handlePressNotificationWarning = React.useCallback(() => {
     if (singleNotifProblem == null) {
diff --git a/src/account/AccountPickScreen.js b/src/account/AccountPickScreen.js
index 86da36f4cc9..adee196ce67 100644
--- a/src/account/AccountPickScreen.js
+++ b/src/account/AccountPickScreen.js
@@ -34,6 +34,8 @@ export type AccountStatus = {|
   // list of problems that are likely to prevent notifications from working.
   // We'll use it to warn on each account item that has problems.
   +notificationReport: { +problems: NotificationReport['problems'], ... },
+
+  +silenceServerPushSetupWarnings: boolean | null,
 |};
 
 /**
@@ -45,7 +47,7 @@ function useAccountStatuses(): $ReadOnlyArray<AccountStatus> {
   const accounts = useGlobalSelector(getAccounts);
   const notificationReportsByIdentityKey = useNotificationReportsByIdentityKey();
 
-  return accounts.map(({ realm, email, apiKey }) => {
+  return accounts.map(({ realm, email, apiKey, silenceServerPushSetupWarnings }) => {
     const notificationReport = notificationReportsByIdentityKey.get(
       keyOfIdentity({ realm, email }),
     );
@@ -56,6 +58,7 @@ function useAccountStatuses(): $ReadOnlyArray<AccountStatus> {
       email,
       isLoggedIn: apiKey !== '',
       notificationReport,
+      silenceServerPushSetupWarnings,
     };
   });
 }
diff --git a/src/account/accountActions.js b/src/account/accountActions.js
index 5a88c3cdf2f..b88d32f43ad 100644
--- a/src/account/accountActions.js
+++ b/src/account/accountActions.js
@@ -6,6 +6,7 @@ import {
   ACCOUNT_REMOVE,
   LOGIN_SUCCESS,
   DISMISS_SERVER_PUSH_SETUP_NOTICE,
+  SET_SILENCE_SERVER_PUSH_SETUP_WARNINGS,
 } from '../actionConstants';
 import { registerAndStartPolling } from '../events/eventActions';
 import { resetToMainTabs } from '../nav/navActions';
@@ -22,6 +23,11 @@ export const dismissServerPushSetupNotice = (): PerAccountAction => ({
   date: new Date(),
 });
 
+export const setSilenceServerPushSetupWarnings = (value: boolean): PerAccountAction => ({
+  type: SET_SILENCE_SERVER_PUSH_SETUP_WARNINGS,
+  value,
+});
+
 const accountSwitchPlain = (identity: Identity): AllAccountsAction => ({
   type: ACCOUNT_SWITCH,
   identity,
diff --git a/src/account/accountsReducer.js b/src/account/accountsReducer.js
index 7feeb42a491..dd47275a1e5 100644
--- a/src/account/accountsReducer.js
+++ b/src/account/accountsReducer.js
@@ -11,6 +11,7 @@ import {
   LOGOUT,
   DISMISS_SERVER_PUSH_SETUP_NOTICE,
   ACCOUNT_REMOVE,
+  SET_SILENCE_SERVER_PUSH_SETUP_WARNINGS,
 } from '../actionConstants';
 import { EventTypes } from '../api/eventTypes';
 import type { AccountsState, Identity, Action, Account } from '../types';
@@ -49,6 +50,9 @@ export default (state: AccountsState = initialState, action: Action): AccountsSt
         lastDismissedServerPushSetupNotice: action.data.realm_push_notifications_enabled
           ? null
           : state[0].lastDismissedServerPushSetupNotice,
+        silenceServerPushSetupWarnings: action.data.realm_push_notifications_enabled
+          ? null
+          : state[0].silenceServerPushSetupWarnings ?? false,
       });
 
     case ACCOUNT_SWITCH: {
@@ -77,6 +81,7 @@ export default (state: AccountsState = initialState, action: Action): AccountsSt
             zulipVersion: null,
             zulipFeatureLevel: null,
             lastDismissedServerPushSetupNotice: null,
+            silenceServerPushSetupWarnings: null,
           },
           ...state,
         ];
@@ -126,6 +131,10 @@ export default (state: AccountsState = initialState, action: Action): AccountsSt
       return updateActiveAccount(state, { lastDismissedServerPushSetupNotice: action.date });
     }
 
+    case SET_SILENCE_SERVER_PUSH_SETUP_WARNINGS: {
+      return updateActiveAccount(state, { silenceServerPushSetupWarnings: action.value });
+    }
+
     case ACCOUNT_REMOVE: {
       const shouldRemove = a =>
         keyOfIdentity(identityOfAccount(a)) === keyOfIdentity(action.identity);
diff --git a/src/account/accountsSelectors.js b/src/account/accountsSelectors.js
index 186a0cb45ad..f3be04ab3f6 100644
--- a/src/account/accountsSelectors.js
+++ b/src/account/accountsSelectors.js
@@ -159,6 +159,9 @@ export const getZulipFeatureLevel = (state: PerAccountState): number => {
   return zulipFeatureLevel;
 };
 
+export const getSilenceServerPushSetupWarnings = (state: PerAccountState): boolean | null =>
+  getAccount(state).silenceServerPushSetupWarnings;
+
 /**
  * The auth object for this account, if logged in; else undefined.
  *
diff --git a/src/actionConstants.js b/src/actionConstants.js
index 58631ce7204..5c354fcd6cf 100644
--- a/src/actionConstants.js
+++ b/src/actionConstants.js
@@ -21,6 +21,8 @@ export const REFRESH_SERVER_EMOJI_DATA: 'REFRESH_SERVER_EMOJI_DATA' = 'REFRESH_S
 
 export const DISMISS_SERVER_PUSH_SETUP_NOTICE: 'DISMISS_SERVER_PUSH_SETUP_NOTICE' =
   'DISMISS_SERVER_PUSH_SETUP_NOTICE';
+export const SET_SILENCE_SERVER_PUSH_SETUP_WARNINGS: 'SET_SILENCE_SERVER_PUSH_SETUP_WARNINGS' =
+  'SET_SILENCE_SERVER_PUSH_SETUP_WARNINGS';
 
 export const INIT_TOPICS: 'INIT_TOPICS' = 'INIT_TOPICS';
 
diff --git a/src/actionTypes.js b/src/actionTypes.js
index fb59b663f0e..ca767b492ac 100644
--- a/src/actionTypes.js
+++ b/src/actionTypes.js
@@ -60,6 +60,7 @@ import {
   DISMISS_SERVER_COMPAT_NOTICE,
   REGISTER_PUSH_TOKEN_START,
   REGISTER_PUSH_TOKEN_END,
+  SET_SILENCE_SERVER_PUSH_SETUP_WARNINGS,
 } from './actionConstants';
 
 import type { UserMessageFlag } from './api/modelTypes';
@@ -176,6 +177,11 @@ type DismissServerPushSetupNoticeAction = $ReadOnly<{|
   date: Date,
 |}>;
 
+type SetSilenceServerPushSetupWarningsAction = $ReadOnly<{|
+  type: typeof SET_SILENCE_SERVER_PUSH_SETUP_WARNINGS,
+  value: boolean,
+|}>;
+
 /** We learned the device token from the system.  See `SessionState`. */
 type GotPushTokenAction = $ReadOnly<{|
   type: typeof GOT_PUSH_TOKEN,
@@ -671,6 +677,7 @@ export type PerAccountAction =
   // state.session
   | DismissServerCompatNoticeAction
   | DismissServerPushSetupNoticeAction
+  | SetSilenceServerPushSetupWarningsAction
   | ToggleOutboxSendingAction
   ;
 
@@ -797,6 +804,7 @@ export function isPerAccountApplicableAction(action: Action): boolean {
     case CLEAR_TYPING:
     case DISMISS_SERVER_COMPAT_NOTICE:
     case DISMISS_SERVER_PUSH_SETUP_NOTICE:
+    case SET_SILENCE_SERVER_PUSH_SETUP_WARNINGS:
     case TOGGLE_OUTBOX_SENDING:
       (action: PerAccountAction);
       (action: PerAccountApplicableAction);
diff --git a/src/common/ServerPushSetupBanner.js b/src/common/ServerPushSetupBanner.js
index ddae8f36653..5e3c466ce99 100644
--- a/src/common/ServerPushSetupBanner.js
+++ b/src/common/ServerPushSetupBanner.js
@@ -6,7 +6,7 @@ import subWeeks from 'date-fns/subWeeks';
 
 import ZulipBanner from './ZulipBanner';
 import { useSelector, useDispatch } from '../react-redux';
-import { getAccount } from '../account/accountsSelectors';
+import { getAccount, getSilenceServerPushSetupWarnings } from '../account/accountsSelectors';
 import { getRealm } from '../directSelectors';
 import { getRealmName } from '../selectors';
 import { dismissServerPushSetupNotice } from '../account/accountActions';
@@ -38,12 +38,15 @@ export default function ServerPushSetupBanner(props: Props): Node {
     state => getAccount(state).lastDismissedServerPushSetupNotice,
   );
   const pushNotificationsEnabled = useSelector(state => getRealm(state).pushNotificationsEnabled);
+  const silenceServerPushSetupWarnings = useSelector(getSilenceServerPushSetupWarnings);
   const realmName = useSelector(getRealmName);
 
   let visible = false;
   let text = '';
   if (pushNotificationsEnabled) {
     // don't show
+  } else if (silenceServerPushSetupWarnings === true) {
+    // don't show
   } else if (
     lastDismissedServerPushSetupNotice !== null
     // TODO: Could rerender this component on an interval, to give an
diff --git a/src/settings/NotifTroubleshootingScreen.js b/src/settings/NotifTroubleshootingScreen.js
index 9111fdafe9e..f09585b1025 100644
--- a/src/settings/NotifTroubleshootingScreen.js
+++ b/src/settings/NotifTroubleshootingScreen.js
@@ -160,9 +160,17 @@ invariant(
 export const chooseNotifProblemForShortText = (args: {|
   // eslint-disable-next-line no-use-before-define
   report: { +problems: NotificationReport['problems'], ... },
+  ignoreServerHasNotEnabled?: boolean,
 |}): NotificationProblem | null => {
-  const { report } = args;
-  return notifProblemsHighToLowShortTextPrecedence.find(p => report.problems.includes(p)) ?? null;
+  const { report, ignoreServerHasNotEnabled = false } = args;
+  const result = notifProblemsHighToLowShortTextPrecedence.find(p => {
+    if (p === NotificationProblem.ServerHasNotEnabled && ignoreServerHasNotEnabled) {
+      return false;
+    }
+    return report.problems.includes(p);
+  });
+
+  return result ?? null;
 };
 
 /**
diff --git a/src/settings/PerAccountNotificationSettingsGroup.js b/src/settings/PerAccountNotificationSettingsGroup.js
index cd06cd933ab..7ae0f2e7075 100644
--- a/src/settings/PerAccountNotificationSettingsGroup.js
+++ b/src/settings/PerAccountNotificationSettingsGroup.js
@@ -5,7 +5,7 @@ import type { Node } from 'react';
 import invariant from 'invariant';
 
 import type { AppNavigationMethods } from '../nav/AppNavigator';
-import { useGlobalSelector, useSelector } from '../react-redux';
+import { useDispatch, useGlobalSelector, useSelector } from '../react-redux';
 import { getAuth, getSettings } from '../selectors';
 import SwitchRow from '../common/SwitchRow';
 import * as api from '../api';
@@ -13,7 +13,11 @@ import NavRow from '../common/NavRow';
 import TextRow from '../common/TextRow';
 import { IconAlertTriangle } from '../common/Icons';
 import { kWarningColor } from '../styles/constants';
-import { getIdentity, getZulipFeatureLevel } from '../account/accountsSelectors';
+import {
+  getIdentity,
+  getSilenceServerPushSetupWarnings,
+  getZulipFeatureLevel,
+} from '../account/accountsSelectors';
 import { getGlobalSession, getGlobalSettings, getRealm, getRealmName } from '../directSelectors';
 import ZulipText from '../common/ZulipText';
 import RowGroup from '../common/RowGroup';
@@ -29,6 +33,7 @@ import { ApiError } from '../api/apiErrors';
 import { showErrorAlert } from '../utils/info';
 import * as logging from '../utils/logging';
 import { TranslationContext } from '../boot/TranslationProvider';
+import { setSilenceServerPushSetupWarnings } from '../account/accountActions';
 
 type Props = $ReadOnly<{|
   navigation: AppNavigationMethods,
@@ -40,6 +45,7 @@ type Props = $ReadOnly<{|
 export default function PerAccountNotificationSettingsGroup(props: Props): Node {
   const { navigation } = props;
 
+  const dispatch = useDispatch();
   const _ = React.useContext(TranslationContext);
 
   const auth = useSelector(getAuth);
@@ -53,6 +59,7 @@ export default function PerAccountNotificationSettingsGroup(props: Props): Node
   const realmName = useSelector(getRealmName);
   const zulipFeatureLevel = useSelector(getZulipFeatureLevel);
   const pushNotificationsEnabled = useSelector(state => getRealm(state).pushNotificationsEnabled);
+  const silenceServerPushSetupWarnings = useSelector(getSilenceServerPushSetupWarnings);
   const offlineNotification = useSelector(state => getSettings(state).offlineNotification);
   const onlineNotification = useSelector(state => getSettings(state).onlineNotification);
   const streamNotification = useSelector(state => getSettings(state).streamNotification);
@@ -61,6 +68,10 @@ export default function PerAccountNotificationSettingsGroup(props: Props): Node
 
   const pushToken = useGlobalSelector(state => getGlobalSession(state).pushToken);
 
+  const handleSilenceWarningsChange = React.useCallback(() => {
+    dispatch(setSilenceServerPushSetupWarnings(!silenceServerPushSetupWarnings));
+  }, [dispatch, silenceServerPushSetupWarnings]);
+
   // Helper variable so that we can refer to the button correctly in
   // other UI text.
   const troubleshootingPageTitle = 'Troubleshooting';
@@ -207,6 +218,12 @@ export default function PerAccountNotificationSettingsGroup(props: Props): Node
             );
           }}
       />,
+      <SwitchRow
+        key="silence-warnings"
+        label="Silence warnings about disabled mobile push notifications"
+        value={silenceServerPushSetupWarnings ?? false}
+        onValueChange={handleSilenceWarningsChange}
+      />,
       ];
 
   return (
diff --git a/src/storage/__tests__/migrations-test.js b/src/storage/__tests__/migrations-test.js
index dc8dd963eff..917cd95ae5e 100644
--- a/src/storage/__tests__/migrations-test.js
+++ b/src/storage/__tests__/migrations-test.js
@@ -105,7 +105,8 @@ describe('migrations', () => {
   // What `base` becomes after all migrations.
   const endBase = {
     ...base52,
-    migrations: { version: 60 },
+    migrations: { version: 61 },
+    accounts: base52.accounts.map(a => ({ ...a, silenceServerPushSetupWarnings: null })),
   };
 
   for (const [desc, before, after] of [
@@ -282,7 +283,7 @@ describe('migrations', () => {
     [
       'check 57 with an `undefined` in state.accounts',
       { ...base52, migrations: { version: 56 }, accounts: [...base37.accounts, undefined] },
-      { ...endBase, accounts: [...base37.accounts] },
+      { ...endBase, accounts: [...endBase.accounts] },
     ],
     [
       'check 58 with a malformed Account in state.accounts',
@@ -299,8 +300,9 @@ describe('migrations', () => {
           ...base37.accounts,
         ],
       },
-      { ...endBase, accounts: [...base37.accounts] },
+      { ...endBase, accounts: [...endBase.accounts] },
     ],
+    // 61 covered by whole
   ]) {
     test(desc, async () => {
       // $FlowIgnore[incompatible-exact]
diff --git a/src/storage/migrations.js b/src/storage/migrations.js
index c0af14ff851..05fbf82387c 100644
--- a/src/storage/migrations.js
+++ b/src/storage/migrations.js
@@ -517,6 +517,12 @@ const migrationsInner: {| [string]: (LessPartialState) => LessPartialState |} =
   // Discard invalid enum values from `state.mute`.
   '60': dropCache,
 
+  // Add silenceServerPushSetupWarnings to accounts.
+  '61': state => ({
+    ...state,
+    accounts: state.accounts.map(a => ({ ...a, silenceServerPushSetupWarnings: null })),
+  }),
+
   // TIP: When adding a migration, consider just using `dropCache`.
   //   (See its jsdoc for guidance on when that's the right answer.)
 };
diff --git a/src/types.js b/src/types.js
index 8c08f70d151..a7e886a2921 100644
--- a/src/types.js
+++ b/src/types.js
@@ -142,6 +142,28 @@ export type Account = $ReadOnly<{|
    * apply.
    */
   lastDismissedServerPushSetupNotice: Date | null,
+
+  /**
+   * The setting to silence prominent warnings about disabled notifications.
+   *
+   * ("Disabled" meaning in particular that the realm hasn't enabled
+   * notifications; i.e., RealmState.pushNotificationsEnabled is false.)
+   *
+   * Users will set this if they want something more permanent than the
+   * ServerPushSetupBanner's "Dismiss" button. That button only snoozes the
+   * banner (for two weeks, as of writing), but this setting makes the
+   * banner never appear. (The banner's information will still be available
+   * on the "Notifications" screen.)
+   *
+   * Will be `null` when notifications are enabled for the realm, or when
+   * we've never had server data for this account. Otherwise false, unless
+   * the user has switched it to true, which they can do until the realm
+   * enables notifications. (If true when the realm enables notifications,
+   * we intentionally forget the `true` by setting this to `null`. That's to
+   * make sure it's false if notifications are disabled later, because that
+   * disabling might be a surprise that the user wants to know about.)
+   */
+  silenceServerPushSetupWarnings: boolean | null,
 |}>;
 
 /**
diff --git a/static/translations/messages_en.json b/static/translations/messages_en.json
index b5a8362a891..12d2b46d406 100644
--- a/static/translations/messages_en.json
+++ b/static/translations/messages_en.json
@@ -255,6 +255,7 @@
   "Recipients": "Recipients",
   "Delete message": "Delete message",
   "System settings for Zulip": "System settings for Zulip",
+  "Silence warnings about disabled mobile push notifications": "Silence warnings about disabled mobile push notifications",
   "Troubleshooting": "Troubleshooting",
   "Send a test notification": "Send a test notification",
   "Failed to send test notification": "Failed to send test notification",