Goof Off is preferable to Goo Gone. They are different products. Goof Off is basically acetone. That, a clean toothbrush and some elbow grease should sort it without damaging the veneer.

Some small pock marks etc are not uncommon in the veneer and generally are not apparent once it's stained and finished. Remember of course it is a natural material so will not be perfectly uniform. The veneer is about .6mm thick, sometimes even less, so very light sanding is recommended to remove any imperfections. Your pics look about average and better than many I've seen so it should be fine.