We wouldn't put working out his sneaky movements past the Starks though - they're a group who have learned a lot in the "Game of Thrones".
Gillen also spoke about how the catalyst behind his attempts to sow discord among the Starks is his history with Catelyn, who spurned him in favor of Brandon - and later Ned - Stark.
As we saw from the letter he planted in episode 5 for Arya to find, Petyr Baelish is no fool. But no one who received the letter in Winterfell back in Season One is alive to prove otherwise. The dragon seemed to rather like Jon.
But could he just be throwing us another red herring? There are still some loose ends (Lyanna whispered something in Ned's ear that we couldn't make out), but the dramatic smash-cut from a close-up of the baby's face to one of the adult Jon Snow's face was obvious. Not just because Littlefinger recognises that fighting style, but because any of the folks now at Winterfell who spent time around the Stark kids before the war could have told him that Arya and Jon were best buddies. So the two are on a slow-motion trajectory toward incest, and they don't yet realize it. But with this character he'll say something and mean something else. Sam blows past this, but if Gilly was in fact trying to read the word "Rhaegar" it would have enormous implications.
Jon is the rightful heir to the Iron Throne.
This being said, Petyr Baelish has mastered the art of staying one step ahead of his enemies, but with Bran's all-seeing powers and Arya's expert stealth, he's fighting a battle that surely he can't win?
Clarification on the R+L=J theory: Fans did not initially believe the theory that Jon is a Targaryen because Jon burned his hand when he killed the first wight in Season One.
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Then a wrinkle entered Littlefinger's perfectly starched plan: the arrival of Arya Stark, who was supposed to be dead. They were attacked by Lannister forces and taken prisoner in season two. Not satisfied, the show creators have dropped in The Hound, Beric Dondarrion, Thoros of Myr and Tormund Giantsbane to make up the greatest dream team ever to venture north into a nightmarish hellscape in order to capture and bring south an undead creature. We also know he's been living a more moral life in recent seasons.
"But to Littlefinger, there's something even worse and more risky about Jon: if Jon isn't stopped soon, Jon is going to completely destroy Littlefinger's throne-taking army by marching it north to die fighting magical snow zombies". Of course, we know the real context for it, but Arya doesn't.
The reason Gendry is doomed is simple: Keeping him around is too much of a happy ending, and that is something Game of Thrones is allergic to. In case you forgot, check out the Season 1 scene below. He'll hope Jon doesn't return from beyond the Wall, but if he does Littlefinger will hope to have Sansa completely against him by then.
Arya saw the wily schemer obtaining an old letter of some sort written by Sansa. Perhaps it is Arya's newfound self-isolation and people watching prowess she gained from the Faceless Men in Braavos that leads her to immediately question Sansa's motives when she does not stick up for Jon Snow in front of his lords. He conspired with Robert's brothers against my beloved Joffrey and tried to steal his throne.
Under duress from Cersei, Sansa wrote a letter telling Robb to bend the knee.
While he chips away at Sansa with his mind games, having successfully turned her against her family, he'll ride into King's Landing at the side of the "Queen in the North". Littlefinger would undoubtedly be missed by the viewers, if not by the characters on-screen.