I think what you mean is the brake backing plate or even the dust cover, right? Well whatever it is there probably shouldn't be oil dripping off it. It could be brake fluid, fluid on a hot rotor or in a drum would make a smell, maybe the line is loose or a seal is out on one of the caliper pistons, but then you should notice the lack of brake fluid in the resevoir or the pedal depressing to the floor. That or the axel seal is out, bout all I can think of, take it to an independent shop and have them look at. I know CAR-X will diagnose a problem for free. Have them document the problem and then take it to the dealer and shove the problem down the service manager's throat.
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