Try some kind of de-greasing detergent like Dawn.

Having just had this same problem, I'll tell you what I did. As barnmom suggested, apply a layer of Dawn or other degreasing detergent to the oil spot with a Q-tip. Allow it to sit for a while, then gently blot with a slightly damp microfiber cloth.

When I did a search online, I also read about making a paste of corn starch and applying it to the oil stain. Wait until it dries and then brush off the powder.

I used Dawn and got good results. I was afraid to leave it too long because it's blue. The results are not perfect so I may try the corn starch paste when I get the chance. Good luck!

Try white chalk, rub on as thick as you can & wait as long as you can before rinsing off. Sure worked for me!
Suzi