Vinegar should do the trick. If vinegar doesn't harm your hands, it is not going to harm the stainless steel. It should dissolve the hard water stains.
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Cleaning stainless steel appliances without having soda water on hand all the time? Try using a softened sponge, wringing out all the water from it, and dip in cider vinegar and gently rub the stainless appliance. Comes out looking beautiful and it's also environmentally sound!