The Duchess appeared in The Muppet Show Episode 506, as one of many characters from the Alice in Wonderland books. Originally appearing in Alice's Adventures in Wonderland, the Duchess is a querulous, intensely ugly aristocrat who oversees a turbulent household, including a pepper-obsessed cook, a Cheshire Cat, and a squawling baby. The Duchess later throws the baby out, who then turns into a pig. She returns, cowed into friendliness by the threat of decapitation, to joing Alice at the croquet match and trial.
On The Muppet Show, the Duchess is a minor figure, appearing in the chorus and background of many scenes. She has a single solo line during the "Smile" medley, and is usually accompanied by the baby. During the courtroom scene, she's holding a piglet, the transformed baby; both serve as proxy Muppaphone keys for judge Marvin Suggs.