[Hawk]

Plus Littlefinger told her that Tyrion said he would release the girls in exchange for Jaime, and Tyrion sent her Ned's bones as a good will gesture. I think she holds hope that Tyrion will do what he said he would and that Brienne will be able to bring the girls back to her.

The main difference from the books, and it is a significant one that I don't know why they changed, is that: (spoiler tagging just in case people don't want to hear book differences, but it is not really a spoiler in that there is no info on events not already covered on the show)

Spoiler!

In the book, both her and Robb are distraught because they receive word that Bran and Rickon are dead, killed by Theon with their tarred heads impaled on spikes on the walls of Winterfell. She loses it and releases Jaime that night. Robb loses it and sleeps with Jeyne (Lady Talisa on the show). Their reckless actions are easier to understand in that scenario, and it would have been easy to include it in the show since Theon did fake the killings on the show too, plus dramatic when they think the boys are dead. One of the few unnecessary differences on the show that really bothers me.