The Parkers were minor, non-speaking characters in An All Dogs Christmas Carol. They were the first human owners Carface Caruthers had when he was a puppy. Only the child was mentioned by name, and that was Bobby.
When, desperately in need to relieve his waters, there was no place to go, Carface did it under the Christmas tree he had knocked over, so Bobby's mother ejected him, and Bobby didn't try to defend him.