Don't know about TC's refinishing service, but Flitz Stick Compound (or Dico) and a felt point and/or cloth wheel in a Forster or Dremel rotary tool will make it like new. It actually removes the top surfaces, how much depends on how much pressure and for how long, so it can also remove pitting without degrading the frames edges, serial number, etchings, etc if they are not too deep. With controlled buffing you can achieve a final finish from satin to a mirror polish on stainless steel.
Years ago I did a Taurus 431 44SPL pre-lock stainless pistol I had to a mirror finish with my Forster and Flitz as above, and it was easy.
FWIW