I used to have a few of those guys as well and witnessed the same very odd behavior. What I read about it seems to point to what Kurt said, that they hold their eggs there until they hatch. However, they are supposedly so fragile that they rarely do hatch.
I understand what you mean about how it looks like the emerald is feeding from it, which is what I thought at first. My GUESS is that they are either rearranging the eggs or pulling things out of their mouths and putting it into their flap, perhaps for nutrition once they become larvae? *shrug*