I had the same problem with a Svend Andersen Worldtime Chronograph. The deep scar on a lug was "inherited" when I bought the watch. This damage did not deter me because I knew that local repairs by laser welding are easy when a specialist handles it. This welding is possible with most materials (gold, stainless steel etc.). Buying a watch in this condition was thus preferred to getting one prepared for sale with extensive polishing.

Theoretically, over-polished cases could be restored by this method. The excess weld material is polished off by traditional methods (lapping grinder machine, e.g.), which means the specialist must also master these techniques and have an eye for the original features of a case. In my experience it is far too risky to entrust big brands with such restoration work, not the least because the communication is too complicated (via AD etc.) to keep it under control as customer. For me, it is important that such repair/restoration work is limited to the essentials. Otherwise I could end up with a watch where the "patina" from use and age of different parts is no longer matching.

I am happy with the repair work on my Andersen and enjoy the sympathetically refreshed watch much more than looking at a scarred one.
Björn