まーごめ is short for まーちゃんごめんね ("Maa-chan, I'm sorry"), a line said by actor Ootsuru Gitan during his apology press conference after he was caught cheating on his wife, Marcia. Comedian Ootsuru Himan (not related to that actor) popularized the phrase by using it in many of his performances, and it became somewhat of a catchphrase for him.

Parody of a recurring intro bit from comedy duo Shinkuu Jessica (真空ジェシカ), which goes like

Kawakita: どうも、〇〇です ("Hello, this is [a random description that actually fits the other guy better]")
Gaku: 言うとしたら僕〜 ("I should be the one saying that~")

Here, Fubuki swaps in her "hard-to-remember surname" trait, while Kirino is the one catching strays.