What is the grammatical term for this? I know it is correct to say: “We appreciate your being here,” rather than “we appreciate you being here.”

I saw a sign at the veterinarian’s office today which reminded me to ask. The sign read: “We appreciate your dog being on a leash.” And I thought, shouldn’t that be: “we appreciate your dog’s being on a leash”?? Or am I hyper-correcting??

I’ve tried to look this up in a grammar book I own, but cannot find it easily. Is it a gerund?