The people I geek out with seem to think that the Stark siblings, Arya, Sansa, and Bran are well aware that Littlefinger is conspiring to create division and that they are creating a reverse sting of some kind, maybe to remove him from the head of the Knights of the Vale without losing the Knight's support. I hope so anyway. Littlefinger seems to be treating them as naive, easily manipulated children when they are most emphatically not those things any longer.