The gryphon event is NOT well designed at all. You get a one time description of what you need to bring and as far as I can tell that's it. But even if you don't forget about it because you wanted to do something first, there's no indication that you need very specific quantities of these items, which again as far as I can tell is not specified anywhere. And until you have that exact amount or more of every item, the button to spend the resources won't even appear.
For reference, you need 2 strong health potions, 5 anti bleeding ointment, 5 meat
Feeding him does literally nothing by the way, other than the flavor text. Hopefully there will be some expansion of this later.