Yeah I know, I understood it as soon as I saw the scene. Was asking my brothers last week if that shit will come back to bite her now that she shunning away LF lol.
Arya, as much as I like her, is perhaps stupid enough to fall for this ploy...
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Unless Arya deliberately confronted Sansa with an open door, knowing LFs female servant spy was listening? Follow him around and make him notice... To make him make a play like this, make him think she is manipulating him? I mean farfetched, but all that ninja training has to include some Macchevellian smarts no lol.