If they are a responsible shop that happens to be familiar with the OOB finish on the BCB they would likely ask you if you wanted it returned to the original finish or if you wanted it returned to roughly the surface you have it at now.
As far as resurfacing goes, they'll probably start with 220 grit wet dry sandpaper or 180 abralon depending on how deep the scratches are.
For an OOB finish they should stop at 400 grit and then take a fine rubbing compound to it. While Lane 1's website does say polished, very few balls produced in Muskegon with solid coverstocks had a high gloss polish OOB.