The dad told "Gina" about his illness, but at the party "Gina" finds out about it from "Leni", then goes to her dad and confronts him about it, and dad doesn't find that at all odd.
In Episode 2, 'Gina' is at dinner with her dad and Claudia when it is revealed that he is sick. In Episode 3, Gina runs to her dad at the party and says that Leni just informed her that he was sick.