The pet is not removed when a player enters a non-pet WorldGuard region if the player is riding the pet.

It is removed just fine if the player is not riding the pet, and it also works if the pet is worn as a hat.

Nevermind, my WorldGuard region just wasn't tall enough. The player only looks like 1 block taller while riding on a pet, but the actual position of the player is actually much higher.