I have a 26-1 .45 Colt that has had a long sad story of neglect. It was stolen and mutilated and recovered before I bought it.
I sent it off to be repaired and refinished since it's an excellent shooter.
When I got it back from repair and shot it the rounds impacted extreme left. All the rear sight adjustment is required to center the group. This was not the case before I sent it in.
Upon close examination the barrel is not centered. It is turned slightly to the right as you look over the sights.
How hard is it to turn the barrel?
Right or left hand thread?
Shipping the gun back to be corrected is a pain the #&2 as I have to drive an hour to ship it.

You will have to find a gunsmith with the right tools for the job. I dont know why they would remove the barrel for a refinish.

Your revolver barrel has right hand threads.

I agree that you need to find a gunsmith with a frame wrench and an N frame insert for it. It just needs a little tweck to center the barrel.

Make the smith show you the frame wrench and insert. You don't want someone sticking an old hammer handle through the frame and banging on it.

__________________
John 3:16
WAR EAGLE!

I have not had S&W re-finish a revolver in a few years, but every single one I have ever done has had the barrel removed when it was re-blued. The factory told me when I asked that question that any reputable re-blue requires barrel removal, factory or not. The factory guy at the time also said something about leaching the bluing solution in the barrel thread area or something like that, and that a re-blue without a barrel removal is instantly noticeable by even a lay person. As I am not a gunsmith, I can only take S&W at its word.

It is, I am told, an acquired skill.