Anything peeling that bad will likely need sanding. Pick a section and start high grit like 1000 or higher then work down til peeling comes off quicker. Now you know your starting point. There is a huge thread here called all about dome polishing and cleaning.
I'm with @Sparky_911 judging from the pictures, I'd probably start at 1K with a wet sanding. Then do it again at 1.5K, then check clarity.. you can then take it to 2K if you desire. After sanding use a buffing compound of your choice, then lastly a good coat of auto wax to seal them.