What is causing the marks. I see some hard water spots but I am not sure if that's what you're referring to.
If waterspots, you'll want to look for a water spot (mineral) remover first. If they've been there awhile, they are likely etched into the clear coat. In that case, water spot remover followed by polishing them out with a polish or light compound that has some abrasives.
I will properly treat it. You will need to remove the wax. Wash the area with Dawn dishwashing soap. Spray the stained area with a 50-50 mixture of water, preferably either distilled water or soft water. Let that sit for about a minute wipe off with a terry cloth or microfiber.
All in one polish with a light cutting pad. Start slow. If your more accustomed to wax, try a cleaner wax. Even by hand I suspect you'd see a world of difference.
DA polisher with a SOFT cutter pad. The good news, is that you can use that polisher to correct, cut, and polish paint moving forward. I use mine to wax my truck
I'm a bit surprised by all the comments that say just go straight to polishing. If they are etched, they will reappear after polishing.
If you don't chemically remove the minerals that caused the water spots, a machine polish drives them into the paint, looks great for about 2 weeks and then they will reappear.