Stains on Poured Floors from the 60s?

I have the same problem with my parents poured floor. The house was built in 1967 and the kitchen and bathrooms have the poured floors. Over the years the countertops and floors have developed stains, probably from some chemical cleaner. The stains are rust-colored, but they are not rust. I don't know what to use to remove the stains since they are under the clear coat finish.

By Linda A.