I'm sure religionists will draw the wrong conclusion from this study. It found that people who feel they were wronged by a romantic partner and pray for the partner's well being are more forgiving than people who don't pray. They compared it to people who just described the partner and others who thought nice thoughts about the person but didn't pray.
The authors say that, among people who had been praying, they found an increase in "selfless concern," which is a generalized concern for all people. They speculate that when a person feels wronged, having a high selfless concern level lets them forgive more easily.
That's the psychological explanation. If you believe in a god who hears your prayers, then if you specifically ask her to help the person who wronged you, sure it's plausible that that would make you go along with what you have asked god to do.
The biological explanation would be that asking god to be nice to someone releases some hormone in your brain that makes you like the person better. Maybe prayer releases oxytocin somewhere.
But I predict that religionists will say it proves that god hears the prayer and changes the heart of the praying person.
In the past, studies showing the effectiveness of prayer in medical cases have been flawed. This does not claim that prayer affects the person prayed for; it says it affects the person who is praying, which is much more plausible.