Hey and long time no see!
This くれる is くれる used when requesting something, similar (but more casual) to ください.
てくれる (or てください) attached to てあげる -てあげてくれる/てあげてください is used when we request someone (2nd person) to do something that will be beneficial for 3rd person.
(I changed sentences a bit for clearance)
フクロウさん「これネコさんに あげてくれる ？」
Mr. Owl (1st person) requests Mr. Crow (2nd person) to give it to Mr. Cat (3rd person). But Mr. Crow refuses, and tells Mr Owl to ask someone else to do that. “it”, the object belongs to Mr. Owl (the first person/speaker/the one requesting).
Mr. Owl asks Mr. Crow if he intends to give it to Mr. Cat. But Mr. Crow says that he is not willing to give it to him. “it”, the object belongs to Mr. Crow (the 2nd person, the listener, the one hearing question (not request)).
I hope it shows difference in this case clearly,
I will change this sentence and add てあげてくれる to the to-do list.