Tutie is a monster who lives at the Faffner Hall music conservatory.
In the Ghost of Faffner Hall episode "Delighting in Sounds", The Wild Impresario searches for new sounds, to participate in the festival of sounds.
He hears that Tutie has the hiccups, and realizes that's the sound he's searching for. Unfortunately, right after he tells Tutie that she'll be in the festival, she loses the hiccups.
The puppet was first seen (with different eyes) in episode 423 of The Muppet Show, performing the song "Your Feet's Too Big".