Clean cast iron sinks using a mild abrasive cleaner and a soft cloth to rub out the mark. Kohler makes a cleaner specially designed for its cast iron sinks, or you can use a general-purpose mild abrasive or other cast iron cleaner. According to Kohler.com, abrasives should be used only as needed because frequent use can damage the sink.
Wash vitreous china and fireclay with a soft cloth and dish soap before trying other cleaners, because it scratches easily. If this does not remove the pot marks, use a small amount of a gentle abrasive on a damp cloth to scrub the spot. Rinse away the cleaner and wash the sink as usual.
Scrub a stainless steel sink with a stainless steel cleaner on a damp cloth, working with the steel's grain. This will buff out any marks and leave the sink polished. According to Kohler.com, stainless steel sinks will scratch if an abrasive is used. You can use a general stainless steel cleaner or Kohler's specially designed cleaner.