Just bought a tux off eBay, and it appears someone tried to remove the pick-stitching on the right shoulder not realizing it was meant to be there. The left shoulder looks fine. Is this repairable without too much cost?
It should not cost more than $100 to repair that.
The stitch looks to be for cosmetic effect since the seam doesn't appear to be overlapped. Not certain if it is an overlapping seam from these pictures. Also looks like a fake hand stitch done with a machine. You can remove the stitches yourself with a pin. Personally, would prefer not having this stitch on a tuxedo.
Each stitch is a loop. Insert the pin in the loop of thread and pull but don't force it. The biggest concern is if you catch the cloth with the tip of the pin you can create snags in the cloth. Be certain you are only inserting the pin into the loop of the thread.
You will need to cut one of the stitches on the unbroken shoulder to get started.
Not familiar with the way this machine stitch works and it may be easier to pull the thread from left to right or right to left across the shoulder so try starting from either direction and see if the stitch releases easier going in one direction across the shoulder compared to stating from the other direction. Once you undo a couple stitches you will get the hang of it. As you remove a few stitches, cut the thread off so you won't have to pull the entire length of thread thru every step.
This can be restitched without opening the jacket and would take around 5 minutes.
The most complicated fix would require opening the lining on the inside shoulder to access the stitch from the inside of the jacket. Even to do this is not a big deal.
Disregard the previous advice, especially about the repair cost