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.
Instead of going to ’Starbucks…I make my own Coffee at home, yell out my name rong, then light a five dollar bill on fire.
So when is this..."old enough to know better" supposed to kick in?