my best guess, ayra is going a strange and roundabout way to show sansa that littlefinger is trying to separate them while also giving her a lot of exposition on her background so sansa gets why littlefinger must die in the next episode and who does it... while also fooling littlefinger into thinking his plan working.
the stuff like when they first saw each other "do i have to call you lady", "yes" that was in line with their character and funny and it was a little chilly because they weren't close growing up. that doesn't translate to falling comically into this trap where all of the sudden they are on the verge of killing each other because freaking littlefinger, who both girls know personally can't be trusted, drudged up a note (that really shouldn't be of consequence anyway).