Grandma Tentacles is Squidward's paternal grandmother seen in the episode "Chum Fricassee." When Squidward was young, she taught him her famous recipes. Squidward later quit his job at the Krusty Krab, and went to work at the Chum Bucket in which he sold her food to people, thus making it a big hit. However, she wasn't too happy about this, and explained to Squidward that if it was cooked for less than 24 hours it causes severe stomach aches. This made all the customers angry at him, and, consequently, they destroyed the Chum Bucket.
The octopus now known as "Grandma Tentacles" was born to unknown parents.
She married an unknown Mr. Tentacles.
She gave birth to Mr. Tentacles, the father of Squidward Tentacles.
At some point, she created the recipe for Fricassee.
In "Chum Fricassee," Grandma Tentacles was shown to be extremely abusive towards Squidward, such as frequently stomping on his foot with her walker and telling the customers to destroy the Chum Bucket.
Despite her rather antagonistic side shown in Chum Fricassee, she was briefly mentioned by Squidward in the episode "The Two Faces of Squidward." Squidward said that she gave him homemade soap thus indicating that she did love and care for him.