Mrs. Grouch is Oscar the Grouch's mother. She is also the mother of Oscar's brothers, Ernest & Otto & Oscar's sister Bunny. She has visited Sesame Street various times over the years, including episode 3141 to make sure that her son is still grouchy & hasn't been turned nice. That same year, she also appeared in the special Sesame Street Stays Up Late, communicating by phone with her son & other relatives.
Mrs. Grouch lives in Illinois. She was the one who gave Oscar his present (the old sneaker) as a baby, as Oscar described in "I Love Trash". Whether she is a widow or divorced from Oscar's father is unknown.
A running gag between Mrs. Grouch & Oscar is that whenever Oscar would say "please", she would wash his mouth out with vanilla ice cream.