Continuity mistake: In one of the opening scenes when Bob comes in from walking the dog in the rain, he dries the dog off with a towel and puts the towel on top of the coat tree. He tries to feed the dog and when it cuts back to the dog the towel is on the floor, then his wife comes in and the towel is back on the coat tree.
Continuity mistake: When Bob is trying to feed his dog in the kitchen, Bob picks up one of the two dog bowls and brings it into the kitchen. In the next shot the dog is looking at the door and there are two dog bowls sitting there, then in the last shot there is only one dog bowl again.
Other mistake: In the second scene in the Gorilla Building, Elizabeth says, "Thank you, Jeff" while talking to Charlie. Thirty seconds later she says, "Thank you, Charlie."
Continuity mistake: When Grace and Bob are coming back from their first date, the first shot of them walking along, holding hands, shows that her arms are not in the sleeves of his jacket and it is merely draped over her shoulders. There is then a shot of Marty moving two of the chairs together. In the next shot, Grace's arms are now in the sleeves of Bob's coat (that way he has more excuse not to have her go through the trouble to take it off and give it back to him). After she slaps him, in the shot of her saying "I'm really sorry I hit you," and then kissing him, the coat is draped over her shoulders again. Then there is a quick shot of Bob's reaction as she stops kissing and says "Bye" and the next shot (where Grace opens the gate and runs into the house) shows her arms in the sleeves of the coat again. (01:11:50 - 01:13:10)
Other mistake: When Gracie gets a heart and she is about to go into surgery she begins to talk to her Grandpa Martie. Watch his lips, he is mouthing her lines.
Continuity mistake: After Grace slaps Bob, his hand goes from being on his cheek to down and then back on his cheek.
Visible crew/equipment: When Bob and Charlie enter the boardroom for the meeting with the suits in the zoo's administration building, the actor's green T-mark is visible on the floor under the table, where Bob stands. (00:33:05)
Answer: Presumably it's a favorite mascot of the group. There's likely no backstory per se, it's just something the filmmakers did to add to sense that these people have been together for a very long time.