I use a magic eraser when I get a few marks on mine, cleans it up beautifully. Although I'm not sure if I should recommend them to use as they might look harmless but they are quiet abrasive. But I find they work wonderful.
Elise, in the EDC under General Tips in the front of the book you will find a section on cleaning for stubborn residues ie1000 vinegar and 1/4 tsp dishwashing detergent added to the bowl - cook for 1 hour/50o/speed 1. Afterwards, rinse the bowl and MC out several times with clean water.I've just made a batch of lemon cleaning concentrate in mine and that leaves the bowl nice and shiny - perhaps you could try that. If your TMX is used a lot it will never look as good as the day you took it out of the box but either or both of these methods will help get some of the lustre back.
May i know how the magic eraser looks likes? Perhaps my place didn't sell such kind of things. =)