Are there any solutions to getting rid of or stop new calcium deposits from forming in back of throat?

Calcium?: I'm guessing that those are not calcium deposits. It's possible that you have pits in your tonsils from 40 years of occasional illnesses and tonsillitis. It's a little gross, but what happens with these is that food collects in little pockets and then putrifies. This gives you little, white deposits that smell bad. You can pick them out, use a water pick, or go all out and get a tonsillectomy.