How do I remove baked-on brake dust without damaging the wheel finish?

Start with a wheel-safe cleaner and iron remover rather than aggressive scrubbing. Allow the chemistry to soften metallic contamination, then agitate with soft wheel brushes and rinse thoroughly. Repeat rather than escalating to harsh products. Strong acids or abrasive pads can damage sensitive, polished, matte or chrome finishes, so identify the wheel finish before choosing a cleaner.