Here we have a demonstration found over at Metacafe which shows you how to wipe out screen scratches on your PDA, Phone, camera screen etc… It works by heating up the egg to 65 degrees C (not higher as egg goes harder at 71 degrees C). You then get a cloth, soak it, put it in the oven and repeat a few times. Once it dries out you have a cleaning cloth which apparently will wipe scratches out (or fill them in). The cloth works for about 100 times and seems like it could do its job. I think I need to try this on my mobile phone screen to see if its true.
Another option is to purchase a cheap screen scratch remover from Amazon costing less than $10.