From Muppet Wiki

Grandma is Gonzo's grandmother. She lives in a ramshackle house with young Gonzo, her daughter Grace, and Grace's son Gander. Grandma is apparently raising Gonzo with Grace's help; there is no mention of Gonzo's parents in the Muppet Kids books.

Grandma teaches Gonzo about good manners in the 1992 book Show-and-Yell.