What colour is the backing? Will rinsing it through make it worse? Can you put the spot over a bowl, put a drop of clear dawn on the spot, rub it a bit to loosen the grease and then pour clean warm water through the spot and into the bowl until it is clean? I would then blot out the extra moisture with a clean white towel the move to the next spot. I would then drape the quilt over furniture until the spots dry.