Spilled teak oil in sink, now it's dry
There are a number of solvents out there that will remove that with no more effort than applying it to the spot. I use lacquer thinner for many problem spots, Goof-off may work, Goo-be-gone, things of that nature that will not even begin to harm the stainless steel. 

Do not use a steel wool pad!!!! Or anything of that nature, a solvent will do it.

To try it, put some on a clean rag and rub the spot a little on the thinnest place the oil is, if the removes the thinnest places, carry on with the rest, if not, try another. 

Come to think of it, alcohol (denatured or isopropyl)is used to prep teak for gluing. It removes the oils on the surface of the wood so the glue bonds better.