I run mosh v1.2 on both Linux and OSX. When I remote to a machine from Linux to OSX, and type 'top' I see the usual stats. When I quit using 'q', I see leftover top output on the screen. When used with SSH, the screen gets cleared. I've tried with both xterm and gnome-terminal.
Here's the dtruss output from the OSX while running top (not sure whether this helps)
write_nocancel(0x1, "\033[1;23H3\033[1;44H09\033[1;58H61\033[133G40\033[2;40H2.79\033[2;52H4.18\033[63G93.2% idle
write_nocancel(0x1, "\033[61;1H\033[?1049l\r\033[?1l\033>\0", 0x17) = 23 0
BTW, this last of clear/refresh behavior not limited to 'top', but vim also doesn't clear the screen when quit.
Mosh currently doesn't support the alternate screen (smcup/rmcup control codes). We're hoping to fix this for Mosh 1.3. You can follow our progress on #2.