Oh my, if washing fails you can just use it for show on the back of your sofa.... so sorry that happened. The maker should know this but how to tell her or him is the question.

While dense quilting will make a quilt stiffer and batting may affect how it drapes, I don't think either would make it scratchy.

Is the thread used for quilting a monofilament? If not, I would also say it's the fabric. Regardless, after being washed a few times, I doubt it will improve much at this point. :(

What is the fiber content. Cotton or something else? Wool or wool batt can be scratchy. If it’s a natural fiber, not poly, it’ll take other solvents beside water and soap. Try alcohol or acetone (fingernail polish remover). If wool, could try lanolin from feed store. No guarantee.

Densely quilted quilts are always stiffer but not sure that they are scratchy. I think it might be the fabric used.

I have the same problem. I have used some fabric backing that was stiff when I bought it. I did use it on a couple of quilts as the backing. I thought it was just sizing, but the fabric has never softened. As long as I use the quilt with other fabric under it, like on a bed, it doesn't bother me, but I don't like it next to my skin. I am thinking about adding a softer fabric as a second backing, using minimal stitching to keep it on the quilt. I thought I would just turn the edges under close to the original quilt binding and hand sew it. Minky is so stretchy, but I may try it

Could it be that the scratchiness is due to a wool batting you are sensitive to?

It's the quality of the fabric she used. This could be a car quilt. One that you use when you go on a picnic.

What about adding a second backing of fleece? I've never had a problem with that fabric.