1. Remove as much of the salad dressing as possible.
  2. Treat with a stain remover designed for inorganic stains of which oil would be one.
  3. Blot as much of it up as possible with paper towels.
  4. Apply a second time and blot.
  5. Then use a heated soil extractor.
  6. Then place a damp white towel over the stain.
  7. Then shoot very hot steam into the towel and you will get what is called “heat transfer” of the remaining oils on to the towel.

That should do it, however, when it dries there may still be residual oils underneath and they could wick up and the process would need to be repeated.