watch when link gets up to track the fly. he has a napkin on as a bib. then when he is about to catch it in front of the dad he doesn't have it on anymore.
If you look at Link when he stands up from the table while tracking the fly, you can see that the napkin is attached to Links shirt on one side only (the other side already let go). So my guess is that the other side let go too when the camera was on Links face (you can't see the napkin at this point) and it just fell off when it was out the camera's reach.