Tyler,
I can barely make it out, but I think I see it on the side view you posted.
If this is the rocker panel, it should be black paint mixed with something to give it a texture, so it withstands the rocks, etc.,, that hit it.
You should be able to polish it down,, but if it were me, I would first get all the white residue out of the scratch and see how it looks, and then decide if you want to go further. Get a toothbrush or something like that that can get into the scratch and not scratch the paint further to clean it out.
Sometimes QTips moistened with the correct solvent, etc., can help move polish out of cracks, crevices, etc., too.
If the owner wants it out, then I guess you have to give it a try- I dont know if it would be good to sand it if the area has a texture, because as you know, the sanding will smooth out the texture and make it more noticeable..
Perhaps, another way to go would be to clean it out, and get some touch up paint in it to help fill it, and let it go. Its in an area that may get hit often - it got hit that time, right?
If this is Jet Black, its easy to get touch up and it fills nicely with a Sword Brush you get from an auto paint store, and some of the correct thinner or reducer, for the type of paint, and just paint it in, a little at a time, letting it dry, until it fills it up. We used to do this all the time in the automotive body/paint shops I worked in..
If the customer wants to pay for Drcolorchip.com, these people have the process dialed in way better than anyone, and the result would be almost perfect and not complicated at all. I have used their system on many different paint colors and they always turn out great, and the paint stays in the scratch and doesnt fall out a year later, etc...
Good luck with this, you are doing fine.
Dan F