The extended couch gag from Sunday's episode started with the family rushing through Manhattan traffic to attend a taping of the Late Show, soundtracked – in what must have been a callout to Manhattan – to Gershwin's "Rhapsody in Blue."
The scene then cut to Letterman's studio: "So what are we doing here?" he asked. "Is this the thing where the family runs in and sits down?"
Right on cue, the Simpsons dashed in, at which point Letterman's animated version lost it: "That's it? We flew you in and put you up for that? I think we're done here. Paul?"
The gag ended with Paul Shaffer's band playing the theme to The Simpsons, before the screen faded to black with the message, "We'll miss you, Dave."