I am wondering ... why don't those women use the old ivory soap to soak those little things in before they wash them? Hey that worked good! I remember I had to iron my baby things. There was very little knit anything but t-shirts back then.
If you want to try and save your tablecloth and napkins. You could try to use a stain remover first. I have saved things I have found like you with Zout stain remover before. My neighbor swares by the oxyclean.