Its never good to use any liquid on the screen but you can try getting a microfiber cloth and spraying (using a fine mist spray bottle) a little bit of rubbing alcohol on the microfiber cloth and try to buff out the circular marks. Other than that i have no clue and would try to get it replaced. Don't put on any screen protector yet.
Just realize I have the same problem with a phone that is a few days old. I already had to send the one I got for Christmas back cause of a pixel problem, now I have this going for me . I didn't notice it until I had my phone off. When the phone is on, I don't notice it at all. It does seem like a manufacturing issue. I wonder if anyone ever found a solution to this problem.
Anyone figure out what this was? I got a new GSM Razr Maxx and I have these same little marks. They're little circles or semi circles that disappear when I clean my phone, but appear with finger prints. I noticed that when I was cleaning my phone with alcohol I could feel them. I've only had my phone 2 weeks and have not dropped it or done anything else to it.