In Season 2, Episode 7 ("A Man Without Honor") of HBO's Game of Thrones, there is a dialogue between Tywin and Arya.
Tywin Lannister: Girl, m'Lord. Low-born girls say m'Lord, not my Lord. If you're going to pose as a commoner, you should do it properly.
Arya Stark: My mother served Lady Dustin for many years, my Lord. She taught me how to speak proper... properly.
Tywin Lannister: You're too smart for your own good. Has anyone told you that?
Arya Stark: Yes.
I'm not sure I understand this. Thus far Arya is concealing her true identity, claiming to be a daughter of a self-taught and educated stone mason, a commoner.
What does Tywin mean by what he says? Does he believe she's not a commoner, and is really of some noble birth by trying to correct her?
I only seek an explanation up to this point in the tv-series. Nothing beyond in the novels.