It happens all the time: A team member brings a complaint about someone else, or maybe a couple of employees are squabbling and folks are picking sides. I've been reading about workplace drama lately, and living a little of it, and it reminds me how much I hate it.
So what do you do?
You could say your hands are tied, that your boss or organizational policy won't let you do anything else. But then you sound helpless and they won't see you as having any more horsepower than they do.
You could join in the complaining or choose a side, but then you're just fanning the flames. That makes it likely there will be more time wasted, yours included.
You could tell the team member to toughen up, and remind him that you don't pay him to like folks, just to get work done. That's a good way to ensure that these things happen behind your back and you never get a chance to stop the productivity loss.
You could ignore the whole thing, just let things slide, and watch your workplace become Peyton Place.
You could tell the employee you'll handle it, and then go fix things with the other person. That will work, but will make it necessary for you to fix every occurrence, every time.
My preference: I tell my griping team members I don't like talking about people, but that I'm willing to talk with them. Then I get the two parties face to face, let them talk and I listen. Once that happens, the solutions usually aren't rocket science.