Official statement denying breach:
As of right now the official statement from TeamViewer is that everything is fine. It's unlikely any vile individuals will give a rats ass about Runescape players, but I know quite a few people who use TV to play on their mobile phones. (especially old tipiters) The reddit thread has recommendations for other programs to use as alternatives, though I'm unsure if they'll serve the same purpose for mobile playing.
Note to mods: While this is more pertinent to Tech and Computers, for visibility and RS account security's sake I'd urge you to leave this in GD.