I noticed that was there after they added the adoption date thing to pet profiles. I think it just means you've had the pet since before they added that feature?

I think is right. I notice all my pets have it on them, but newly created pets don't.

(Legacy) means they were added to the site prior to the adoption day thing being added. It's nice to know when pets birthday's are I guess. Here one of my pet's birthdays is Halloween, my favorite holiday and I didn't even remember.