Get a bag of those red shop towels, they are great for various things, among them, tires from vehicles not maintained with water based products. No sense in ruining a good brush for nothing. The red rags do a good job of scrubbing on most tires. Anything that is super contoured/has those lines gets "No Touch" from me.
Maybe they're using clear silicone I'd keep some of that Griot's rubber prep with a few grout sponges for cases like this. I've been waiting for my next major order to pick some up, but there is a thread around here with about half a dozen raves about the product's ability to clean off old tire dressing gunk with minimal effort.