She wants to help him in secret. The dad is probably keeping close tabs on his son so if she gets close to him, the dad will get suspicious and start investigating. Plus if he does find out about her power he wouldn't be able to lie to his dad about it.
Because of ian's father's powers something like eye of the truth or idk what's it called basically he can see riche's energy/mana traces (he saw riche's mana/energy on her brother in the hunting competition and he go crazy. See chapter 16) that's why he was able to find riche in the first life and torture her resulting to her death. So now riche's is being careful to get involved in Ian's family but she also wants to help ian so she's doing it in the sidelines.
....why are you doing this? Why are you hiding? Is that guy who possessed your guard told you to hide your identity? I thought you wanted to help your squirrel friend asap? So you need to save that child first and foremost, since that seems to be the reason why you enrol right? Or am I mistaken? Did I miss a chapter?