Can I stop iPhone apps from changing my Gmail status?
I'm going to assume that you mean this app: https://itunes.apple.com/us/app/phone-for-google-voice-talk/id541829441?mt=8 Since the app is free, it's reasonable to have ads. You could email the developer and ask for it to be removed in the next release. 

Or, if you don't mind losing the Google Voice integration, you could go with Verbs ($1), which is an IM app.

Less reliable way to fix it: After signing in with Mo+ GV, sign into Gtalk from somewhere else (like your computer). I think only the most recent status will be displayed.

Insane way to fix it: Jailbreak your iPhone to disable code signing. Then, find the "I'm using Mo+…" string in the application's binary and change it to an empty string.