The K-1766 salt test will precipitate a lot of silver chloride as part of the titration. The silver chloride is very abrasive and will get embedded in the plastic which causes build up. The best way to clean it out is to add cleaning ammonia to it (the stuff you can buy in any hardware store or supermarket). Ammonia will dissolve the silver chloride. The easiest approach I find is to do the salt test, rinse out the sample tube when done and then add ammonia to it and put it back on the speedster for a minute or two and then rinse the ammonia out. Rinse well and let it dry.
In general, when testing, you should always rinse your sample tubes thoroughly under tap water after each test and allow them to dry. You should never just do the test, discard the liquid and then put them away. Triple rinsing all lab ware is the best way to keep sample tubes clean. I have my original Taylor sample tube that is over 7 years old. Aside from a little bit of scuff marks at the bottom from the magnetic stir bar, it looks as good as the day I got it.