That gun doesn't look as bad as I envisioned from your original post. I tend to agree with JDW on the best path to pursue, but depending upon the extent and depth of any pitting, a lot of people would go whole hog and do a total refinish or restoration. However, you would forever lose the wear and character that was put on the gun by your relative. And there is a big difference between refinishing and restoration. A good restoration would make the gun worth more, but might cost as much as the gun is worth, or more. A refinish... especially a poor refinish... might actually make this gun worth less than it is right now. But a good and proper clean-up done by someone who has the tools and ability could make your gun look much more presentable.
I have not removed the buttstock from an L.C. Smith for at least 10 years, but as I recall, disassembly to properly refinish the wood is tricky and requires proper tools and techniques to get the top lever shaft aligned with the trigger plate upon reassembly. Your screws look mostly unmolested, and you would need good gunsmithing screwdrivers to make sure they remain that way. Just removing the lockplates when they are closely inletted and stuck in the wood can do damage if you do it wrong. Cleaning the wood with alcohol can remove all of the old shellac right down to bare wood, and it is extremely difficult to apply new finish with the metal still attached to the stock. If you did end up removing all of the old finish, steaming out most of the dents would certainly improve the appearance if you could avoid the temptation to improperly sand the wood. But on the other hand, slopping a bit of shellac on the metal will not cause irreversible damage. I have no clue what your abilities or gunsmithing experience may be. I just know that a lot of people with good intentions end up doing more harm than good. Often times, less is more.
