From what I see in the pic, it appears to me that the barrel suffered a good whack on a pointy rock or something, the "dent" portion of the damage may have raised and the remaining crater edges were filed down flush, leaving the "divot". That's my longdistance picture assessment anyway.
From the looks of the barrel finish in this area, nearly no original finish remains, just some patina. It also appears that the divot is very shallow. I doubt that removing it by filing will significantly reduce strength. If it is very shallow, I wouldn't bother with the TIG welding, just have whoever refinishes the barrels drawfile it out.
