Devin these are some replies I found for a person who asked about removing the stains from a countertop. Not sure if it would apply to your floor as the floor material would have to be take into consideration but it should be OK for the sink.
"Ferric chloride is used as an etchant for copper and other metals and is usually acidified. When the acid is neutralized, you are faced with ferric hydroxide which is one of the most insoluble compounds known. So you have a brown stain maybe almost black depending on the other things in the ferric chloride.
The least dangerous treatment that I can think of is Iron Out. Iron Out is a powder which you dissolve in water and apply. Do not expect instant results and depending upon the aggregate used in your top, you should test it an inconspicuous location to make sure it doesn’t decolor your counter. 24 hours is not an unreasonable time to wait. Don’t let the spot dry during treatment. Maybe build a little dam of Non-Staining plumber’s putty and keep it wet.
You can also try CLR with much the same cautions but in my experience, CLR is second tier.
You can try Cirtic Acid (available in hobby supply stores in candle making) in much the same way (making ferric citrate which is soluble). I think there is citric acid in Iron Out but I’m not sure.
Finally, with great hesitation, you can try hydrochloric acid. This is available at the big box home stores as muriatic acid. You must respect this acid! It will burn your skin, blind your eyes and vapors will burn your lungs. If you must try, look for precautions online and plan cross ventilation."
Eric
