Is it permissible to re-swallow a small amount of food that has come back to the front of the mouth due to burping during prayer?

It is not permissible to intentionally swallow anything that reaches the mouth during prayer. If one swallows it after being able to expel it, their prayer becomes invalid. The Malikis held that if vomit was pure and the worshiper swallowed it due to an overwhelming urge or forgetfulness, there are two opinions regarding the invalidation of their prayer. However, if they swallowed it intentionally, their prayer is invalidated without dispute. If the vomit was impure, the prayer is invalidated. Prayer is not invalidated if some food or water comes out with a burp but does not reach the mouth, and then is swallowed.