That phrase is correct and very informal. Backwash refers to someone's saliva that would go back into a drink they were drinking from. There isn't a similar word for food, so you might say something like I don't share food someone took a bite from already. Or you could say something like, "no, you already bit that".
The closest similar slang to backwash I can think of is double-dipping which refers to dipping a chip or something into a dip like ranch or hummus, biting off part of the chip, and then dipping it back into the dip again.