White Car, little black speckles (dots) on the trunk area?

Without seeing it these kinds of things are impossible to diagnose but.....as a guess, based on your description, I would suggest that the damage has been caused by some kind of acidic fallout and has pitted the paint. Now you are probably getting pinpoint rust spots starting. Stripping the whole area and complete repainting is probably the only permanent cure. Or picking up a "new" trunklid from a scrap yard.

Of course, the problem may be something different.

New car dealers in northern states get this complaint all the time.

If you live in a salted community, it is very common. There are always some iron filings mixed with salt. I presume they are from the machinery that busts the salt down into rock salt? Anyway, if you get the area gently buffed out, it should remove the filings which are merely stuck in the clear coat and won't do any damage to the base metal anyway. One point to note; if you garage your car, yet drive it in the winter, the problem is amplified, due to the unlikelyhood that the stauff gets washed off on its own during smows and rains.