The compensator is largely packed with ordinary chassis grease. Dismantling is straight-forward. Clean up every part, smother the parts with fresh grease, and reassemble with new split-pins. While it is in pieces, you can clean and regrease the brake cable, without having to dismantle it (since you can slide it through the conduit far enough to clean). The compensator casing is held together with 3 unusual flanged studs, 2 of which double as pivots for the bellcranks (I think the flanges are soldered on). On my unit, they were fitted with self-locking nuts and spring washers. Spring washers should not be fitted under such nuts. Confusingly, while these studs are 3/8 BSF threaded, the small bolts that also fasten the casing, are 2BA items (also with self-locking nuts).
The final task is fitting the shoes. Mine looked hardly bedded in - let alone worn - even though they had done at least several thousand miles. That might mean that they were not providing the full braking forces for a long time. Refitting shoes is always a struggle. The springs have to be hooked onto both shoes before installing them. My technique was to then hook the top shoe in place, and then prise the lower one onto the adjuster with a large screwdriver. Then I used a length of plywood to press the lower shoe down, and with the help of the screwdriver, slip it onto the expander. Be careful not to injure your fingers if the shoes slip off.