Rust on stainless steel is usually caused by contamination with ordinary steel. Those steel particles leave an undesirable 'red rust' mark and can then become a site for pitting corrosion, so the easiest way to remove the rust is to remove the iron oxide from the contaminating steel.
A number of proprietary solutions are available based on either phosphoric or acetic acid. Stainless steel is quite resistant to mild solutions of these acids, whereas the corroded carbon or low alloy steel is not.
In cases of gross rust contamination, mechanical techniques such as grinding, abrading or shot blasting may be required. These remove more metal and will affect the visual appearance.