I disagree, but that comes down to writing reasons as opposed to actual in story reasons. By this point, with so many superpowers basically being on the stark family's side, it seems silly for Arya to get taken in like that. We're quickly cleaning things up here, I don't see Littlefinger winning.
Also, another side note, how is it that Jon went to the wall without ever stopping in Winterfell, especially when he knows Arya is alive now? The journey alone would have necessitated stopping somewhere, Winterfell would have been the best place.
Maybe he avoided it so that he could focus on getting his task completed, but still... Seems strange for them to save the reunion scene for after he comes back from the wall.
Also, another side note, how is it that Jon went to the wall without ever stopping in Winterfell, especially when he knows Arya is alive now? The journey alone would have necessitated stopping somewhere, Winterfell would have been the best place.
Maybe he avoided it so that he could focus on getting his task completed, but still... Seems strange for them to save the reunion scene for after he comes back from the wall.