If pitting is the only problem with the gun I wouldn't worry too much. Unless the pits are halfway through the barrel metal, they aren't necessessarily going to make the gun unsafe to fire. The .38 is a low pressure cartridge, in comparison, think about how many rifles you've seen that have dovetails cut into the barrel for rearsights, or screws in the barrel to attach the magazine tube- in comparison, the pitting in a .38 revolver has removed a very small amount of metal.

Having a pitted barrel isn't necessarily a death sentence for the gun. At best, it will shoot normally with no problems, at worst it will foul up quickly meaning that you can't shoot it accurately for many shots before having to clean out the lead or copper from the barrel.

If there is nothing mechanically wrong with the gun, I would shoot it and see how well it shoots. If you get bad fouling, you could try using a mild abrasive like Brasso or JB bore paste on a tight patch to scrub the barrel until it smoothens out a bit- this will remove a bit of metal and change the bore dimensions slightly and can dull the rifling, but if the barrel is shot anyway you have everything to gain and nothing to lose.

I have an old military mauser that had a bore that was so badly rusted and pitted, that you could barely see through the bore- it was a terrible shooter and shredded patches that I ran through the bore. I scrubbed the bore with brasso until the patches were able to go through the bore with no resistance from pitting grabbing the fibers, now the rifle shoots pretty decently. This is an extreme example, but goes to show that pitting though undersirable, doesn't necessarily kill a firearm.