This clip both baffled me and creeped me out. It took me a really long time to come up with an approach for it which worked.
My first impulse is to explain everything, you know? Is this a world of uptight cat people? Is this an elaborate dream a guy is having about his grandmother, who turns into a cat when the guy’s cat crawls into his bed? Is this a political allegory where cats and dogs (or mice) are playing out a Revolutionary War drama?
I hit on the poetry angle because she simply looks like she’s reciting. I dragged the tattered shreds of my English degree out of mental mothballs and with Wikipedia’s help I started reading English poetry of the Romantic era until a solid idea for a joke formed. At that point, the backstory didn’t mean as much and the important points explained themselves.
I have to admit that there’s a hidden joke behind this punchline. I actually lifted it from an episode of Teenage Mutant Ninja Turtles. Shredder adopts a powerful interdimensional ally who only eats priceless Ming vases, which the bad guys have to steal to keep him happy.
Rocksteady: We gotcha anudder vase. (Pronouncing it like “case”)
Interdimensional Being: It’s a VOZ, you Philistine!
…Lest you labor under the misapprehension that I am being highbrow or something. Turtle power!