Nobody's lips look the shit in that thumbnail. And I don't mean literally, I mean very rarely, so nobody bother finding the one uggo whose lips do to prove some kind of point. If you look at actual black people, you'll find black people's lips are not really THAT big despite the persistence of this visual stereotype. They're full and round, much closer to the left pic in the thumbnail, not monstrously large. But artists have been exaggerating them often to racist effect for centuries now.
What always gets lost in this discussion is that outrage at this misrepresentation is not new. It's not some tumblr sjw thing, activists have been complaining about racist black caricatures literally since the early half of the 20th century, when the NAACP was formed.
I don't know this character or care about this specific controversy. And she isn't ALWAYS drawn in the caricatured way, just when she's trying to jumpscare the children character, from what I'm reading. That appears to be many critics' issue with it, not the exaggeration in a vacuum. The implicit message is "your black features make you scary," or funny at best, a tired narrative rooted in racist propaganda.
People get so "triggered" by stuff like this because of the historical associations. The well is poisoned by centuries of propaganda. I have to agree that it's hard to look at the image on the right and not see something of old-timey coon caricatures. Add to that the double standard of white features being caricatured much more rarely or not at all (as is the case with the white caretaker in this manga), and never with any agenda.
I don't think the artist has malicious intent, Japanese just tend to do this more than Westerners because they don't have the same history with it. I do think she's playing on racist stereotypes whether she intends to or not.
The question is, does it matter? Does it need to be fixed? Like I said I don't care in this specific case, it's for a Japanese audience so whatever.