The Github App doesn't have any contact/report issue ability. I think it would be nice to have an option from the app's menu to report issues from within the app.
Would a direct link to this issue list be enough? That's how I report issues from within the app.
It would be a start.
I think the best to have is some kind of GitHub's Issues integration, and, provided the app is hosted on GitHub itself, well, use that feature to report bugs for the app.
But a button taking you here would be a good first step.