Speaking of the catgirl being a minor...
Sex aside, that means that there's another aspect at play here - abduction laws.
IIRC taking in a minor without the permission of their parents or legal guardian is considered abduction, even when the minor in question agrees to being taken in. Minors cannot legally consent to this.
Meanwhile, our catgirl here clearly grew up human and had a mostly human life so far. The flashback showed her at various ages in school. She has a smartphone. She had her clothes and undies mailed to Iori's house. All of those things imply that she has a traceable identity.
Had she just been some supernatural creature with no legal identity nor any legal presence in human society, it wouldn't have mattered that she's a minor. But she did apparantly live as human for much of her life. So there's official records somewhere showing her identity, age, and official adress.
All it takes is someone filing a missing person report on her, and our man Iori is gonna be in deep shit...