I love that he has ignored the letter. Cersei deserves what she gets. At one point he wonders if she'll even be alive before he returns. The casual nature of his thought is startling compared to the intense love and protective nature he had for her previously. Her...indiscretions have sparked another change in Jaime and I like it. When he interrupts Lord Bracken he has a conversation with his woman and, at one point, his thoughts drift to Myrcella. He thinks about how he "will need to tell her too" and it is obvious that he plans to tell his children that they are not Baratheons but rather the offspring of his incestuous relationship with Cersei. Prince Doran would not be happy to hear this though I doubt he has any intention of marrying his son to Myrcella and I would wager that he already knows that she is a pureblood Lannister.
His goal is simple...to agree to terms with Tytos Blackwood and have the castle under Lannister control before the day is done. This is the last holdout of the Stark uprising and it's sad for me to see it fall. It's just another reminder that Robb and Ned are long dead. I just know that the Starks will rise again somehow since Arya, Bran, Rickon, and Sansa still live, but I don't think it will happen for some time still.
Once in the castle with Lord Blackwood Jaime offers the terms and Blackwood accepts them almost too eagerly. I don't suspect a trap or a lie. I think Blackwood is just accepting the reality of his situation. I kind of respect that, but it was weird how he kept asking about how and when he'd have to kneel. He was so focused on that. Maybe it means nothing. Jaime gets to see the massive heart tree within the castle and Blackwood tells him about how ravens cover the tree every single night and have been for thousands of years. No one knows why. Perhaps the ravens are connected to Ser Brynden and they return because of his connection to them through the tree. I wouldn't be surprised if he can use them as his eyes as they travel across Westeros. Jaime seals the agreement by taking Blackwood's son as a hostage. The scene at the end where his son grins about being a hostage was kind of funny. Jaime quickly grounds this boy's expectations and reminds him that the only thing keeping his head on his shoulders is his father's continued submission and loyalty. I could hear the way Blackwood snarled the name "Kingslayer" when he said it.
The squabbling of the Blackwoods and the Brackens is ridiculous. Even Blackwood's son sees it from the histories. I could feel the boredom and annoyance that Jaime must have felt having to act as a mediator to these two men.
Martin finishes the chapter in typical "holy crap" fashion as Brienne of Tarth rides up to speak with Jaime. He immediately notices her facial wound that she received from Biter. She tells him that she has found Sansa and that he must come alone to save her from the Hound. There's only one way I can react to that (and I must do so in the epic words of Admiral Ackbar)...