Spoilers from S07E07:

We saw that Littlefinger is sentenced to death by Starks (especially by the law of Lady Sansa Stark) for the crimes.

Wouldn't be more profitable if the three (Sansa, Arya, Bran) consider this character guilty on their own (in private), and order Arya to execute the sentence and at the same time take his face?

If they do it they can rule the Vale and have another links to influence people.