The same person that gave the spoiler above says that the complication is that "Jaime is done with returning people because he wants to stay in KL with Cersei (and in case you’re wondering about their deathbed-side reunion, it’s as gross as you’re imagining). Brienne is all “But, honor, ser!” about it and Jaime is all “Pfft, honor.""
(Little Questions That Don't Fit Anywhere Else - Page 13 - General (GoT) - A Forum of Ice and Fire - Page 13)
She has only seen the first 3 episodes, though, so my guess is that Jaime comes to his senses by episode 4, when Oathkeeper happens.

No one will convince me that the writers were not trolling with that "Are you sure we are not related?" comment by Jaime.

I’m not quite sure where the info that it becomes obvious she has a crush on him came from. I saw it mentioned, but I was purposely avoiding spoilers before I saw it myself. I don’t think there was anything to overtly unless I totally missed something, however their scene together was really great!

The overall tone had the just right amount of tension while still making it clear that they respect each other a lot.

Basically Brienne was pressing Jaime about upholding his vows to Catelyn, and Jaime was trying to explain why he hasn’t done anything about it yet. He talks about how Arya is probably dead and Sansa is married to Tyrion, so what does she expect him to do, kidnap his own sister-in-law? Where would he even send her that would be safe, etc. etc.

Brienne was her beautifully stubborn self and continued challenging him to uphold his vows. She was excellent- really committed. At one point she even said something like “Look me in the eye and tell me-" and I forget the exact phrasing but it was great to see her standing up for herself and what she feels is right!

Her pestering made Jaime remark “Are you sure we aren’t related?” because you’re annoying me as much as the rest of the Lannisters! You’ve got the right hair etc.

Also, regarding the crush thing- if anything I was getting rather flirty vibes from Jaime, as he teased her. He was definitely standing pretty close as he commented on her appearance.

Anyway- It definitely made me happy and think it will for most of you too! Though Jaime was teasing her, I think it was very clear that he’s really frustrated by the situation and his inability to do what he promised. His hands are really tied but he is clearly not happy about not following through yet.

Also, while Brienne was pressing the point, it was clear from her that she’s not truly angry at Jaime, just the situation, and she still hasn’t let go of her somewhat black and white, right and wrong way of looking at things, which is great. It basically made me feel great that they can talk to each other with respect while still being themselves. They’ve definitely come a long way and it is beautiful.

And it set things up nicely for what is to come in episode 4, for sure!