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This unnamed woman is the girlfriend of George Cooper Jr., Sheldon's brother.
She is mentioned in "The Matrimonial Momentum" when Sheldon calls his mother to tell her that Amy broke up with him. Mary tells Sheldon that he should not give her grandmother's engagement ring back yet since Missy is married and Mary will not let George Jr. give the ring to his girlfriend that he's dating, to whom Mary refers as a whore.