When in doubt, try baking soda
You probably won’t be surprised to hear that I am an advocate of the 99-cent and dollar stores. They are great places to pick up items that are, basically, “generic” in nature (though I also find name brands there). One of the things I buy there regularly is baking soda, usually at 2 for $1.00 and sometimes even 3 for $1.00. I keep baking soda in both the kitchen and the bathroom, and have cleaned just about everything with it, including my teeth! Today I used it on the stainless steel sink in the kitchen, and it looks fabulous. Best of all, baking soda is just abrasive enough to give you a bit of scrubbing power, but it does not scratch!