Make a baking soda paste with water and baking soda.. use a soft toothbrush over the piece then rinse and dry with a soft cloth
I sell a lot of silver on Ebay. Jewelry, silverware, serving sets. Silver polish like Wrights and dips like TarnX tend to remove some of the metal. The foil method doesn't work that great and still leaves a grey film that still needs to be removed. I use white toothpaste (not gel) and a damp toothbrush. For large items I use a damp cloth. Also works on copper, brass, gold, porcelain, ceramics, sneakers, plastics, etc. For my sales I needed one product for cleaning everything.
I use a silver cleaning cloth.
white toothpaste on an old soft toothbrush or WEIMANS silver wipes sold on Amazon.
But Wrights silver polish, and use a soft cloth. I would not use toothpaste as it is abrasive. I have used Wrights on lots of my jewelry. Worked great.