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Katy Perry features in the episode, probably because of a controversy in Sesame Street where she was wearing a dress that was said to be revealing too much cleavege. An interview with both Katy Perry and "Sesame Street" writer Joey Mazzarino stating that she was actually wearing a flesh-colored shirt underneath it. In the Simpsons, however, she wears a red dress with some of the Simpsons's family on it.
The book Homer wants Maggie to read is called 'A Fluppet's Christmas carol', a parody of The Muppet Christmas carol possibly linking to the Katy Perry controversy of Sesame Street.