Mee, for all of her self-absorption, will protect Brenna to the death; she frequently offers to bite anyone that she feels may be bothering her pet. In her mind, Mee owns Brenna as do other Shees who are bonded to humans. It's a terrible thing for a bonded Shee to lose their pet; often they die from the pain of separation.
She doesn't feel like her obsession with Crab is irritating anymore than Brenna feels her obsession with Talon is. For her, crab is divine and by rights, it should be given to her several times a day.