I believe it's a reference to Kogasa's SoPm article, where she claims to be a 'babysitter' completely oblivious to the fact she's not scaring anyone. The kids actually love the umbrella and find it amusing.
Whoah, you're a lot stronger than you look!?Boogity boogity boo!♪Boooo!...Huh?...Uh, ummm....S-so...are you...surprised...?Bunbunmaru...S-somebodyyyy hellllp meeeee...Cut it ouuut.You shouldn't be wanting such weird things, okay?Or...?Stop it, stop it! Stop, you're stretching the tongue! Look, it's crying, so don't—! Hey, j-just a...!...Wh-...just a—! Ah! W-what!?Eh? It looks cool!? You want it!?I-I see. Well, that's very n-...I mean, no! It's nice of you to say so, but if you walk off with that, my identity will...ah! Stop, don't pull on it like that...!