The monkey says (very quietly) "Judy," a reference to earlier in the film when Agent Philip Jeffries walks into the FBI Office and says "We're not going to talk about Judy. We're not going to talk about her at all, we're going to leave her out of it," right before sharing his experiences in the Black Lodge. Like most story elements of Twin Peaks, there are as many theories as to what "Judy" means as there are people who saw it.
The name Judy occurs once in the series under unusual circumstances, after Major Garland Briggs has been kidnapped and drugged by Windom Earle. As he later recovers at the sheriff's station, he seems not to recognize his name and questioningly replies "Judy Garland?" However, it should be remembered that this was the name of the actress who played Dorothy in The Wizard of Oz (which was heavily referenced in Lynch's then-most recent feature, Wild at Heart), and probably not meant as a reference to a character in the later film.
In the recently released feature The Missing Pieces from the Twin Peaks Blu-ray set, a longer version of the Jeffries scene is found, which contains a few additional clues. Jeffries is seen checking into a hotel in Buenos Aires, whereupon the hotel clerk gives him a letter left for him by Judy. Later, when he mysteriously appears at FBI headquarters, his line "I found something...and then there they were" is expanded into "I found something, in Seattle, at Judy's...and then there they were." The scene as it appears in the finished film is intercut with the scene of the various otherworldly characters (such as BOB and the Man From Another Place) in such a way as to imply that these beings are the "they" of which Jeffries is speaking. One could therefore infer from the longer version of the dialogue that the convenience store these characters were said to live above might have been Judy's, or that she lived close by.
Whatever the meaning that the viewer attributes to the name, co-writer Robert Engels, in an interview with the Twin Peaks fanzine Wrapped in Plastic, has stated that Judy was in fact Josie Packard's sister, who was involved in dealings with Agent Jeffries and ex-Agent Windom Earle in Buenos Aires. This plot thread would have apparently been expanded upon had there ever been any subsequent Twin Peaks movies.