I did the same thing on our first time out with our Classic.
Was able to get most of them out using a Porter Cable Orbital Variable Speed, foam pads, and three stage 3M Compound. Polishing with the "grain", back/forth not up/down.
If you can't feel the scratch with your finger nail you should be able to get most of it out.
"Sticks & stones can break your bones...and hail will dent your Airstream"
So when is this..."old enough to know better" supposed to kick in?