I can't really tell what's going on from the pics, but I'll assume it's some sort of correctible marring (sanding scratches, rotary holograms, etc.). I will caution that I seem to find a lot of flaws that are *under* the paint...prep-work scratches that can only be fixed by completely redoing the area in question. I almost always just live with those (after expressing my displeasure to the shop that did the work).
My first inclination is to take it to the shop and discuss it with them. But don't just leave it there and let them do who-knows-what to it...point out the problem and get an explanation about what's wrong. Then find out how they'd propose to fix it. If that sounds funny, then say you'll think about it and check back with us. If it sounds perfectly reasonable (e.g., "it's a sanding scratch. We need to polish it out with this product...it's a mild abrasive that doesn't contain fillers so we'll know for sure that it's really fixed") then watch them do the work and don't accept results that aren't satisfactory to you. Don't let them work on the whole thing, just the area in question. Be careful that they don't just slop on some filler-rich glaze and say it's fixed.
DIYing this will, IMO, require products far more aggressive than Scratch-X and I'd allocate an hour for the work (not saying it'll take that long, but I want you to go into it with that timeframe in mind). I want to prepare you for the possiblity that this will take a lot longer than you'd ever expect, so don't give up after 20 minutes.
Fixing this stuff by hand isn't easy but I've had decent results with the right products. One of those, 3M PI-III RC 05933, is discontinued and getting hard to find. The other product I've used, 1Z Ultra/Extra Polish, leaves wax behind, so it might not be the best thing for a fresh repaint, well, it oughta be OK if you use some rubbing alcohol or something to remove the wax when you're finished polishing (which will also show if the wax is concealing any left-over scratches). IIRC others have done OK with Menzerna PG by hand, but the 05933 and the Ultra/Extra are what's worked for me. I'd do the first passes with cotton terry before switching to foam or MF (the terry will make things even more aggressive).
All of these products are a bit aggressive, and they'll leave some hazing/micromarring behind. They will almost certainly require multiple applications and I don't mean just three or four or eight (I've spent a *long* time doing this sort of thing by hand, it can take well over half an hour to do a single small area). You just keep going over the area, buffing off the residue, inspecting the work....over and over until the current problem is replaced by the light hazing/etc. from the aggressive product. Then you use a milder product to remove that hazing. That secondary polishing oughta go a lot faster, maybe only four-six passes.
For the second step, I use the also discontinued 3M PI-III MG 05937 but 1Z Paint Polish would be a good substitute if working by hand. It also leaves wax behind so I'd clean that off with the rubbing alcohol or the Deep Crystal Step #1.
Use a fresh-paint-safe glaze over the repainted area for a few months.
Summary:
Aggressive product: 3M PI-III RC 05933 or 1Z Ultra/Extra. Or maybe something else along those lines- a fairly aggressive product that's been shown to work OK by hand.
Milder product: 3M PI-III MG 05937 or 1Z Paint Polish. Or maybe something else along those lines that's been shown to work OK by hand. You do want some corrective ability but also a decent final finish.
