Its only after the Vulcan princess has left the Enterprise that McCoy realises that her adorable parting gift, a chubby brown teddy bear with fangs, was alive.
Ignoring for a moment that he had no idea what to do with the creature (except maybe chucking the thing out of the airlock) there's a ship wide ban on pets of any sort.
While the fluffy thing that's currently curled up on his desk looks friendly he doesn't want to risk it, well aware of the damage Kirk's beloved pet tiger Terry had inflicted upon escaping the confinement of the captain's quarters. While it was unlikely that the thing would be able to consume two red shirts (Terry had been much bigger after all) he doesn't want to have to go through that much paper work again.
Finding no other alternative he does the logical thing and ties a pink bow around the bear like creature and leaves it in Spock's quarters for the Vulcan to find.