Gingerbread Man's arm, leg, and face mask are made of Elven Gingerbread, which is incredibly strong. It's as tough yet as flexible as Kevlar, and G-Man can control it with his mind. However, given the fact that human enamel is tougher than steel, conceivably if you had enough time, you could gnaw off a piece of it and eat it.
This is how it works. IDC if nobody asked.