Baby wipes in my experience will clean almost anything. Engine oil from your hand etc. So if they don't shift it, perhaps the marks on the screen might be permanent. I'd be wary what you try as some screens are easily scratched or scuffed which is why you use a microfibers cloth. http://labnol.blogspot.com/2006/11/wipe-clean-lcd-screen-laptop-monitor.html
I think you really need to post a photo of this screen.