Got frustrated not understanding the fluff reference so down the Internet rabbit hole I went.

After some searching the most likely reference seems to be Banana Nababa, a freeware video game: the game consists of six boss battles, fifth boss/level being named "Gatekeeper".

342
Huh. And here I thought it was just a simple knock-knock joke. Nice find! —
Oh, I found this joke in the wikipedia: —
I am quite sure that Gatekeeper is a reference to Ghostbuster and Zuul, the Gatekeeper of Gozer. Especially with that hellhound-like look. —
Is that why the flavor being "Banana who" a sort of response to those who say it's from Banana Nababa? —
Knock knock // who's there? // banana // banana who? // knock knock // who's there? // banana // banana who? // knock knock // who's there? // banana // banana who? // knock knock // who's there? // banana // banana who? // knock knock // who's there? // orange // orange who? // orange you glad I didn't say banana? —
^^ —