Teak
I had the same situation a few years back. At the end of the season, and prior to the boat being wrapped I very carefully removed my Teak Handrails. I took them home and used the two-part Teak Cleaners that everyone had suggested. As you found the black still remained. I used a Black and Decker Mouse sander (hand sanded as well) and lightly sanded all of the teak. I tried to remove as little as possible. When I was done they looked brand new. I then bolted them to a piece of plywood, and applied a few coats of Cetol. Three seasons latter they still look great. The only problem I had in the entire process was in re-mounting I used Butyl Tape. I had purchased two rolls, and did not realize they were slightly different. The port side went back in perfectly, the excess trimmed off exactly as expected. For whatever reason I used the other roll on the starboard side and it looked and acted the same until I went to trim off the excess. It would not come off. When I contacted the manufacturer he had me check the part number on the rolls. Turns out one is used in some serious industrial applications, like mounting glass in high-rise buildings. The one I should have been using for both is the correct one used in RV applications. Next season I plan on removeing both handles and doing the same procedure over the winter, that is if I can remove the starboard side without removeing the fiberglass. Because I used Cetol, and they still look great I will only have to brush on a fresh coat of Cetol, no sanding should be required. If I was a better painted I might not have to remove them at all, but excess Cetol is almost impossible to remove.