Closer to the books, when Cat and Ser Rodrik go to King's Landing, Cassel finds Ser Aron Santagar (master of arms at the Red Keep) to ask him about the dagger. We never learn what Rodrik learned. Just what did Ser Aron say when asked about the knife? Did he corroborate what Littlefinger told Cat, or did he plead ignorance of the weapon and its owner?
Ser Aron most likely told Ser Rodrik that Littlefinger owned such a weapon, but not much more.