Burn marks in bathroom

I have some burn marks on my bathroom sink vanity. I have only used a white sponge to try to remove them. I was afraid to scratch the porcelain. The sponge lessened the marks-but they are still there & HIDEOUS! I really don't want to have to replace it. Not so worried about scratches-- I JUST WANT THEM GONE! Any thoughts?
Burn marks on porcelain sink
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