In this episode Littlefinger is trying to cause chaos within the ranks of the Starks. He’s meeting with Bran in private, giving him the dagger used to try and kill him, observing Sansa becoming worried that Arya is a master swordsman now, and still scheming. And again, the episode called attention to the ravens and by extension the complete records Maester Luwin kept of all messages sent to Winterfell that Maester Wolkan commented on. After his behavior in this episode, there may be another very valuable letter in those records.
While Sansa is a captive in King’s Landing Cersei has her write a letter to Robb Stark telling him to come swear fealty and that her father Ned is a traitor to the crown. Luwin explains that it is written in duress, and obviously a Lannister ploy. However, that is not on the letter itself and out of context that could be a damaging letter if revealed to the Northern lords and perhaps her siblings. It’s in her hand writing that her father is traitor.
Littlefinger is becoming increasingly desperate. Bran parroted back to him his “Chaos is a ladder line”. Arya is starring at him like she knows what he did and has demonstrated she might be the best fighter in the castle. Jon has no love for him at all. Sansa is only path to keeping his head with the wolves circling and sniffing around him. That letter, of Sansa calling Ned a traitor and Joffrey the rightful King and made Robb come South, might be his only source of leverage to have Sansa protect him. Keep him safe or he exposes that she wrote her father is a traitor.
This a scheme likely to fail, however Littlefinger needs to get the attention off him and fast. Sansa can easily explain why she wrote it and how it was a terrible mistake she naively thought would save her father. It may be his last ditch attempt save his head from being put on a spike over the gates. A fatal mistake.