If the clearcoat truly has been burned through, then there is no wax/protectant to fix this. Your only bet is to apply another clearcoat layer to the entire body panel.
If the clearcoat has not been penetrated, but maybe a slight buffing/compond mark as you mentioned, you may be able to fix it with some rubbing compound and a buffer. Your hand and Zaino will not work. It usually requires a special pad anf buffer. Any body shop/professional detailer should have them.
My advice: Head down to a reputable body shop and they can tell you right away whether the clear coat has been damamged. If not, then buffing should get it out in a matter of minutes.
Good luck!
-Wayne