The twins believed Ringo's Diary to be the coveted object and were trying to convince her to give it to them. But half was stolen by a woman on a motorbike (Spoiler: later revealed to be Yuri Tokikago) right after Shoma and Ringo fought, and the other half was extorted off of her by Masako Natsume when Masako threatened bodily harm toward Shoma and Kanba.
Spoiler: In the last episode the Penguin Drum is revealed to be the fruit of fate that Kanba and Shoma shared while in the box. They give up on their fate to give Himari a new life where both of them do not exist. Their existence is erased and facts are slightly remade to fit this (like Ringo and Himari are still friends but meet in the metro). The two boys in episode 1 talking about the fruit of fate are also revealed to be Shoma and Kanba after the reset.