What skill applies to a player handling a domesticated monstrosity?

This question is prompted by this answer, which argues that Animal Handling is a wrong skill for managing an INT 3 monstrosity, a Grick tamed by some goblins.

A more common example case of this might involve handling a Griffon mount.

If a player wants to handle (approach, pacify, tame) such a monstrous mount/beast of burden/pet, what ability check should a DM call for?