Jaime was more offended that they gave Brienne a wooden sword; not that they put her in a bear pit. Because he knew she could have taken that bear with a proper blade.
Jaime jumped in the bear pit and Brienne didn’t break down thanking him for saving her; she fought him on who was going to be protecting who.
Jaime bent down and let Brienne use his back to get out of bear pit (Why this imagery speaks to me I don’t know, but it does. The fact that’s how he helped her out.), and she in turn saves him by pulling him up out of the bear pit.
Speaking of earlier episodes
Jaime and Brienne were (to my memory) the first Game of Thrones couple to be naked in the same room and not having sex. They were also given the same amount of naked screen time with similar shots; they didn’t show more of one over the other.
Brienne, by herself, took on three men while Jaime stood to the side and watched; protecting herself and him.
Brienne bested Jaime in a sword fight.
Jaime lied to protect Brienne, even though it ended poorly on his end. So in turn, Brienne attempted to stop Jaime’s torment and help him.
Basically, I’m rehashing all of this to bask in the glow of the perfection of these two being kick ass and equally so.