This slip-up was made in the episode where Rory goes to see Jess in New York (Lorelai's Graduation Day)

Rory and Lorelai are listening to music and talking like always and the phone rings. Rory picks it up. She doesn't want her mom to know so she tells him to hold on and tells Lorelai that she's going to talk in her room because it's too noisy. When she's walking to her room, you can still hear the phone ringing. But it stops when she starts talking to Jess again. Part of the song...I think not!