Exactly what happened to my 03 Odyssey. I didn't change the parking shoes and when the weather got warmer it would expand and drag causing lots of thumping / banging. This is really caused by worn parking shoes that are no longer round or match the new rotors. Had to loosen so that the gap was so great when applying the parking brakes it would depress all the way down. On hills it would slowly slide and engage the parking / transmission shift lock in order to stop.
One rear caliper dragged again so it was metal to metal in no time. With new rotors, pads and parking shoes and cleaning the inside of the caliper (piston still highly polished) the issues went away. The parking brake can be tighten so the travel is further up during engagement.
With yours the rust from the rain and with warmer weather decreased the gap in the parking brake shoes and rotor. Increase the gap and the problem should go away if that is indeed the problem. The deposits on the rotor surface is very minor and should not cause the thumping.
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