Miss Tuffsy was a snail owned by Granny who went missing before she took in Gary in the episode "Have You Seen This Snail?" and the book Where's Gary?, under the mistaken belief that he was Miss Tuffsy.
Role in episode
Granny mistakes Gary for Miss Tuffsy and treats him as if he were her: they go shopping together, go to a beauty salon, listen to music, and watch movies. After Gary realizes her plan to fatten him up to his death, he escapes her house and goes back to SpongeBob. Granny follows him and then picks up one of the alley snails that Gary met in the alleyway, mistaking them as well for Miss Tuffsy.