How can I remove surface scratches from a glass coffee table?

There is a solution that you put on glass

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Get a soapy dishcloth and leave on the label overnight. It should come off with a hard edge (thumb nail etc) in the morning. Failing that cigerette lighter fluid is perfect. Just over a pound from any good newsagent. Make sure you get fluid and not gas. Also, take some ID with you look young, you need to be 18.

i dont think you can remove scratches made on glass. but you can cheat by flipping over the glass (unless it's a fixed glass table). that way, the scratches would be on the other side, and since the glass is relatively thick, you would not see the scratches anymore.

try some Bon Ami polish along with some fine steel wool.