Dellinger:
A little information on stainless steel "quality".
First off, most people think of stainless steel (SS) as being rust-proof or corrosion-proof, IE; it will not rust when exposed to air (oxygen) or corrode when exposed to chemical salts (like sodium chloride) AND that it is non-magnetic, even though it is ferrous (contains iron). This is true to a certain extent, but it is dependent on the chemical formulation (type or grade) of the stainless steel. Metallurgically speaking, MOST quality SS contains some percentage of chrome and nickel. The higher the percentage, the better the resistance to rust and corrosion. The trade-off is the initial material cost and higher manufacturing cost due to the difficulty of its ability to be machined or welded. Food-grade SS is usually type 302 or 304 (common for food industry or most commercial applications, like fasteners) Surgical/medical-grade SS is type 310-316 (common for medical devices and high-end cutlery and surgical equipment). What most people do not know is there is a type 400 series (402-409) that has NO chrome and IS Magnetic. This is the "cheap" SS that most Chinese-made consumer products are made from because it is less-expensive material to buy and easier to machine and form (lower manufacturing cost), hence the term "cheap" or "inferior". It may not rust, but it will corrode (unless you get into the more expensive type 410-420). Easiest way to check on what type of SS you are buying or have is to place a magnet on or by it. If it is attracted to it, you probably have a low-type 400 series SS. "Less-expensive" kitchen cutlery, utensils, and pots and pans from China are notoriously made from this material. In this case, you do, indeed, "get what you pay for", which is why European-made kitchen ware is generally 4- 6 times more expensive than its Chinese knock-offs.
You mention the term "oxidation". This term is sometimes used synonymously (IE, as a similar or equal descriptive meaning) for the term for "rust" or "corrosion". Perhaps a better term is "fading". I`ve seen paint that is not rusted or corroded, but it is faded or oxidized from UV-exposure. Removing that "oxidation" is a mechanical process of abrasion where the dead (oxidized) layer is physically removed to expose the "live" layer underneath. This is also accomplished chemically if it etched and/or burned away (like Klasse AOI ). Or you can combine the two together, which is what most chrome and metal cleaners/polishes are.
You are correct in your assessment of scratching or marring SS when attempting to remove oxidation, despite SS being very hard. Most trim is made from sheet metal that had a finish or pattern applied to it during its material manufacturing and is purchased that way (IE, brushed aluminum or brushed SS) BEFORE it is formed into trim shapes. Any circular polishing with a metal or chrome polishing compound will cause marring against this pattern or "grain". Linear hand polishing with the grain or pattern lines, is generally the only way to accomplish removal of the oxidation. I would think a mild (IE, fine abrasive) metal polish, like German-made Simichrome or USA-made MAAS along with a short-nap chamois-like microfiber cloth might be used to do this. A true chrome cleaner or, God forbid, an aluminum polish are probably too abrasive.
(More than you really wanted to know!)