Why did the Natives kill the bad guy for Glass?

I'm not sure I got it. Glass is close to killing Fitzgerald, but stops because of "leave revenge to God" thing his Native friend had told him earlier. Then he pushes him in the water to float down to the Natives on horses nearby. The head Native then kills Fitzgerald. Then the Natives slowly continue on their way, passing by Glass. There's a woman on a horse behind the head Native man.

Question: Was the woman Palowqa, who the Native had been looking for throughout the movie? Is that the same woman that Glass had saved earlier (the one being raped)? Had she maybe been able to tell who Glass was from that distance so that she told the head Native, her father? So the head Native man killed Fitzgerald to say thank you for saving his daughter? Is that it?