When I first noticed the 'staining' which was kind of an odd brown color I figured it was residual oil burning off from the muffler's manufacturing process, as a light oil helps with sheet metal stamp & die process as well as helps with preventing oxidation.
I sprayed Oven-Off on the rear section of the muffler, let it sit for ~1 hour, and used a soft (blue) scour pad and the discoloration went away relatively easy. I then polished this section with steel polish, using a drill with an attached polish pad, and it came out looking pretty good.
I did this approximately 6 months ago, after driving it/owning it for a month. I did notice just yesterday that it is starting to turn slightly brownish again, not as bad as the first time. I figure this may end up just being one of my cosmetic maintenance procedures I'll end up doing a couple time a year.
At some point I'd like to have a chrome muffler and everything behind it in chrome e.g. the tail pipe tips. This would go good with my color scheme.