The oil from the underlayment soaked in to the concrete. You will need to get a good citrus degreaser and follow the instructions. It may work and it may not.

How long has the pad/carpet been gone? If only a short time, it would be good to wait and see if it gets better. It may just be moisture that was trapped by the rubber pad.

The 'finished' concrete is susceptible to the same issues with rubber as other flooring. Concrete is porous. Man-made rubber products contain plasticizers which keep them flexible. These plasticizers are often petroleum based (or soy oil...doesn't matter oil is oil is oil) which means the oil has moved from some thing 'dry' to something porous.

The OTHER issue that might be happening is the concrete has a 'finish' on it of some kind which has had a chemical reaction with the rubber backing. This is TOTALLY possible. Like all 'finished' floors, the finish is a chemical. And chemicals react with chemicals.

My question is: how were your floors PREPARED and then how was the concrete FINISHED? What have you been given as maintenance products for your concrete? Do you need to polish them every few months? Do you need to 'refresh' them every 2-3 years?

And how long have you used the concrete as a finished floor? How long had the rug pad been in place?

Did you find a solution to fix this? I have the exact same problem!

How did you remove it ? ! My washing machine rubber left similar stains !