I totally disagree.
Littlefinger didn't know it was arya.
If he did he'd have capitalized on it in some way. That's who littlefinger is.
The whole point of that scene is that she's in maximum danger, and we see glimpses of who she's going to become.
She leaves king's landing as a girl, dressed as a boy, hiding the fact that she's one of the most wanted individuals in westeros.
Tywin noticed right away that she's a girl, and figures out that she's high born by the way she says my lady instead of m'lady. She pulls the my father was a stonemason and my mother worked for a lady thing. She even has a great move where she says her mother taught her how to speak proper... then immediately corrects herself and says properly. That was her beginning to learn how to play the game of faces.
That's when jackin hagar offers her 3 names. Look at who she picked. Not tywin. Not joffrey, who had her father killed. She didn't get revenge. She made selfless choices. The tickler, because he was torturing people to death. The guy who was going to report her to tywin because she was trying to help robb. And the guards to help her friends escape. All of her choices helped people who were in danger. The opposite of her choosing merin trant over the gambler.
And the scene with littlefinger was the most difficult test. He was one of the most cunning spy masters alive, suspected something was off, and she had no choice but to be in the room with him while he tried to catch a glimpse of her face.
Compare that scene with her tip toeing through a library full of wights later, and you see she's always has this uncanny ability to move around without being noticed. It's part of what made her an ideal assassin.
People complained about arya killing the night king and not using her faceless man skills to kill cersei. But i think they're missing the point. She did use the faceless man skills to kill frey. The guy who betrayed her family more than anyone. She used her stealth that we saw with her learning from cats and overhearing varys - someone else who should have been very difficult to spy on- to sneak past the wights and white walkers and get close to the night king. Even back in episode 1.1 when bran is practicing with the bow and an arrow suddenly hits center target from out of nowhere. She used her fighting skills that we saw with the waif and brienne to finish the job, but it was her stealth that made her able to do it.
And after all she learned from the hound, the last lesson was to go home and not let revenge consume her like it had done to him.
Would i like to have seen her wear another face? Sure, if it was a slow, methodical assassination. But her arc was one of the best prepared in the show, and that littlefinger scene was a prime example of who she was becoming.
