On gryphon anatomy

Gryphons have the pointed, hooked beak associated with a bird of prey.

They also have mammalian teeth.

Conclusion: gryphons have two jaws which can move independently. The beak functions as a highly specialized incisor, and food enters the mouth in the same manner as Earth's birds of prey, but once it's there, it can be masticated by sets of molars specialized for seeds. This makes gryphons look unsettling when they are eating, as the motions of each jaw may not be synchronous.