She spent the entire episode apologising and hoping that she could be with the team again. She wasn't at her funniest or most scathing, but she was vulnerable and that was important. It can be extremely difficult for a strong person to submit to the judgment of another, but it's absolutely necessary to make yourself vulnerable that way in order to establish connections with the people you care about. The defining moment for me was when Gibbs said, "I know," and Ziva responded, "The point is, now I do too." What she really did throughout this episode was to say, "You knew better than I did. I was wrong."
It's a hell of a hard thing to do. But it's also incredibly important to validate the other people in your life this way. It's not enough just to change your mind - you have to be completely open and honest with someone, and tell them that you've come to understand their point of view.
Abby did that too, in the midst of railing at Ziva for not trusting Tony. Even though she was yelling at Ziva, she also admitted that maybe what Ziva had done was understandable, and therefore forgivable.
In the end, Ziva had to bare her soul to Gibbs in a desperate attempt to prove that she trusted him. That turned out to be what he needed in order to trust her again. The payoff for Ziva wasn't just getting her job back, it was getting a family. I think that's worth a little soul-baring.
