What "game" do Kaira and Armpit play when they leave the hotel restaurant and what does Kaira disclose to Armpit?

After they leave the restaurant, Kaira and Armpit play "ditch the doofus." The doofus is Fred. Kaira and Armpit run through the hotel's grounds, eventually slowing down to walk hand in hand. Kaira tells Armpit about her relationship with El Genius and her plans to fire him. She also tells him about the Billy Boy letters, adding that she received one at this hotel.