Gordo & Butter Theory
I think Katie adopted Butter because Gordo was afraid of her and she wanted a dog of her own. I'm not saying Tom is a better person than Katie (I think they deserve each other) but I do think Gordo trauma bonded with Tom. There are little moments in S3 & S4 that show Gordo speeding away from Katie and over to Tom.
I've reach out to the dogs for comment, but no response yet.