"Fuzzy Memories" (Making sense of Chapter 10 and possibly beyond?)
The Backwards House is fighting back against characters' memories more than you might initially think. Just because you remember your name in the Backwards House, doesn't mean you remember everything about yourself. But you can remember if certain things ring a bell to what you forgot.
Catie says their memories have been fuzzy ever since they got to the Backwards House, and while they forgot, the game show's final round helped them to remember they were a dancing prodigy. After the game show ends, while not as vivid, Catie feels a bit of deja vu when Od-Dog calls them "quite the liar" as a vision of someone who bears a striking resemblance to someone we see in a flashback at the end of Chapter 10.
A flashback that ends with Catie calling said someone "liar" being echoed in context to this interaction. A friend it appears? Catie and their friend talk about getting second place in a dance competition because Catie couldn't catch their friend at the end of their performance.
Catie remembers their proficiency at dancing because of a dance competition happening, but they aren't the only one to remember something. When Catie and Od-Dog finish their performance, Od-Dog briefly remembers when Catie catches him only to forget when they accidentally drop him after it's announced they got first place. With Chapter 10's flashback, this confirms Catie's friend is Od-Dog! But then why doesn't Catie remember their friend? Fuzzy memories.
I purpose this theory. Od-Dog got trapped in the Backwards House and Catie went looking for him. But since they got trapped too, Catie doesn't remember who Od-Dog was in real life and that they were looking for him at all as the Backwards House blurs one's memory unless the situation jogs it.