Parasol Lady being the girl from Shiori's past seems all but certain, honestly. The big question is if she still wants Shiori dead or not. While her sending the Tanuki girl after them could be seen as an attempt at violence, someone this versed in monsters (notice she seems to recognize Ayame's 'eloquent mouth') must know that a weakling Tanuki couldn't possibly be a threat to Shiori. Perhaps she's trying to hurt Hinako to get to Shiori? But then, why send someone who's target is mostly Miko, and had no intentions to harm Hinako except as a desperate measure? A lot of things don't seem to quite add up, but at the same time her having a change of heart doesn't seem to add up either. Hopefully we'll get a perspective chapter for her eventually.
That said, if her goal really isn't still to kill Shiori, will that remain the case when she learns Shiori gave blood to Hinako?
Could be she sent the Tanuki as a scout/test, to find out who all/what all is in the area. Basically a sort of Monster Recon, before showing up herself.
I'm curious as to whether she would still want Shiori dead, myself - that feels like the most plausible reason for her character, given what's happened up to now. Going after Hinako would make sense if that is meant to "hurt" Shiori, in the event, she can't actually kill the Mermaid, herself. Though that would assume that she knows how important Hinako is to Shiori--which, again, could be info gained through the Tanuki.
I'm betting that, if Parasol is the girl from Shiori's past, she will undoubtedly be an antagonist, and will be an enemy that Hinako specifically will have to face, forcing her to further accept her feelings for Shiori.
(at least I hope that's the case; there's merit in her saying "I need Shiori alive so she can eat me", but I also hope it forces her to confront her emotional feelings for Shiori, as well. And vice versa, of course.)