Ah, Hinagiku might interrupt that genjutsu. The bird isn't so fast the Hina cant catch it, but she's only keeping pace with the birdin case Furijia gets hurt. That's also why she's so calm about the situation.
I'm creating a mini Naruto and Gamabunta moment, where Furijia needs to get accustomed to riding the bird, and gain its respect. Filolials grow angry if they don't have a weight attached to them, so if ahe refuses to ride it or refuses to let it run theyre not gonna have a good summoner-summoned relationship.
TR; DR Furijia will solve the problem herself, its just a nice gag moment to lighten the mode.