Spoilers from S07E07:

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

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

If they did it, they could rule the Vale and have other links to influence people.