Yeah @anon30627475 I think this is the key: we’ve seen twice already (the taking of Casterly Rock and the original finding of the note by Arya) that the showrunners are more concerned with giving the audience a ‘twist’ than making it sit correctly in the world of the story.
So it could easily turn out to be some massive game for Littlefinger’s benefit the two are playing even though it’s farcical they’d play that game in private like this.
I mean this week we discover that Arya kept the note that Littlefinger hid. I mean what? She’s gone to all that trouble to sneak in there and then she takes it even though you’ve got to assume Littlefinger will check it’s still there every day, right? It’s like basic 101 espionage.