Well I just finished cleaning up the bathtub. The ceramic trims that sit up against the three walls that extend around the edge of the bathtub, were a pain in the ass. They were held in position with grout, but they were also water sealed with silicon caulking. That silicon caulking attracted the evil black mold. Trying to get rid of the mold, was hopeless.
So I removed all of the sections of trim, and gave them a thorough cleaning, via use of all sorts of tools, including a file. Removing each of them from around the bathtub, took ages, and removing the grout and other trash from each of them, took ages as well. I then put them back but used a grout that did not require an additional seal to be added. I used just grout since the black mold never seemed to be attracted to grout.
Anyhow, it looks as good as new.
Well worth the time and effort.