Hypnotism (and psychology) were popular plot elements in film and radio productions at the time.
Cinema audiences would have recognized the nods to popular radio and film personalities of the time, though modern viewers might not easily make the connection. In the years before TV became a household fixture, radio programs provided in home entertainment, from musical to dramatic to comedy, and more.
Babbit and Catstello appear as different animals in each of their three cartoons shorts where they featured from 1942-1946. They First appeared as cats in "A Tale of Two Kitties" (1942), as mice in "Tale of Two Mice" (1945), and finally as mice again in "The Mouse-merized Cat" (1946) although Catsello is hypnotized to believe that he's a dog).
Fluger's Deli is a pun on the famous old NYC restaurant, Peter Luger Steakhouse, originally founded in Brooklyn in 1887.
Final appearance of Babbit and Catstello (Bud Abbott and Lou Costello spoofs) as a feature in Warner Bros. cartoons. The pair would reappear for Warner Bros. roughly 50 years later, and go on to have a few cameo appearances in The Sylvester and Tweety Mysteries.