She had previously appeared in a Sesame Street News Flash sketch in 1982 as Little Red Riding Hood's granny, performed by Cheryl Blaylock. Cookie's grandma also made an appearance in a Monsterpiece Theater story, Little Red Riding Cookie, performed by Joey Mazzarino. These could be different grandmothers from the one who appears in Sesame Beginnings.
Cookie Monster's Grandma was mentioned in the Home Video Cookie Monster's Best Bites as he calls her on the phone. In the book 100th Day of School, Cookie prepare to give trail mix to his grandmother. In a Cookie Monster sketch, Cookie reveals from a card that his grandmother calls him "Little Cookula."
Sesame Workshop press release
Cookie Monster's Grandma takes great pleasure caring for little Cookie Monster. They have a very warm and loving relationship. She helps Cookie Monster's parents out by watching him during the day and cares for her grandson with old-fashioned monster values. She has a hard time keeping up with her energetic grandson but enjoys his enthusiasm. She has endless patience. Grandma Cookie Monster loves her show tunes and sounds a lot like Ethel Merman.