Doubt you will remove it satisfactorily, i had years of chips and scratches on my MB coupe (quite rare) screen, phoning local screen co's (not the heavy advertisers) for a cash price led to a new screen going in @ £175 IIRC.

I had a similar problem a few years ago caused by a defective plastic ice scraper (the plastic holder had an edge that contacted the glass). The problem wasn't too bad until the sun was on the screen and then I really noticed the marks. After hunting around I was advised to use toothpaste! Yes, it worked, just a gentle grinding compound really (with a lot of effort too). It all depends on the severity of the marks. Standard cheapo toothpaste from the supermarket and soft cloths and effort. Good luck.