I've treated garters for mouthrot using diluted Hibiclens (you can get it at most CVS or WalMart). You're going to need to swab the mouth out a couple times a day until he's looked normal for a week or two. Hibiclens is milder than Betadine, so you may want to switch after a bit.
If it's truly mouth rot, you'll see an almost cottage-cheese like residue in the mouth. If you don't see this at an advanced state it's probably just a run-of-the-mill infection, which is easier to treat.