To remove the black marks off of a porcelain sink you can use some vinegar and dish soap.
First clean the porcelain sink with a sponge and dish washing liquid soap.
Then dry it off with a clean dry towel or something.
Then you spray the black mark with undiluted white distilled vinegar and then let it sit for 10 minutes.
Then use a scrub brush or a sponge to scrub the black mark off the porcelain sink.
You might also need to use some baking soda and pour the baking soda on the black mark and then spray some vinegar on it.
Then scrub it with a non abrasive sponge or scrubber.