Though Littlefinger gained the upper hand on Rodrik and Catelyn by learning of their presence when they tried to stay hidden, he remains unaware of the reason for their visit. Littlefinger’s assertion that the dagger belonged to Tyrion directly implicates Tyrion in the crime of conspiring to kill Bran. Since Catelyn is predisposed to dislike the Lannisters, Littlefinger’s claim aligns with the picture of the situation that Catelyn has already begun to paint in her mind.