@havelmom
Chita has something of a crush on Anjou. It's not outright stated but it's heavily implied. So she's angry at Seto because she thinks he basically stole Anjou from her. So this chapter is Chita warning Seto not to "hurt Anna" while giving him the third degree.
It was kind of obvious from her previous appearances that Chita like Anjou and disliked Seto so I don't know why the author dedicated a chapter to spell that out.
I also find these characters kind of annoying; the person who thinks they deserve to be with one of the romantic leads so they belittle, bully, and give shit to the other romantic lead. They don't add much to the story except be an unnecessary obstacle for the main romance. One of the only times it worked was the times it happened Ore Monogatari, when they treated all parties involved seriously, not just "Isn't it funny that one of our main leads is getting cock-blocked/clam-jammed by this character."
Granted Chita hasn't tried to "break them up" (even though Seto and Anjou aren't dating, but you know what I mean), so it's not the worse case scenario that the author could do with this character archetype. However the fact that this chapter all but confirms that Chita's bitter that Anjou likes Seto and Seto has Anjou "all to himself" makes her seem like an entitled jerk, in my eyes.
Your mileage may vary with this character, and that's fine. I just find to be sort of annoying.