To get ready for the release, I've been doing a little research on the show.
I came across this little bit of information on why the Warner Brothers, Yakko & Wakko, always yell out "Hello Nurse!". I found this posted on Michael Dare's Animaniacs Page.
Mr. Dare used to be a writer on the series:
Years ago, Tom Ruegger was asked by Steven Spielberg to come up with new Warner Brothers cartoons. Ruegger invented Tiny Toons, which took place at Acme University, where all the old Warner Brothers characters taught classes to new, younger Warner Brothers characters. Since Bugs Bunny would be teaching a class to up-and-coming cartoon rabbits, the first character Ruegger created was Buster Bunny, who was to be the new Bugs. Ruegger wanted to come up with a new version of Bugs Bunny's famous catch phrase "What's up, Doc?" but all he could come up with was "Hello Nurse!" It just didn't make any sense for Buster to say "Hello Nurse," so the whole idea was dropped.
Years later, Ruegger was once again asked by Spielberg to come up with new Warner Brothers cartoons, only this time completely original. Ruegger invented Animaniacs, and finally found a use for "Hello Nurse."