I would finish my top, stay stitch around the edges just inside 1/4 inch binding seam allowance. I would then take it to the bath tub, run lukewarm water in with my soap for mud and hand agaitate the quilt top until the muddy prints come out. I would then drain the tub. Fill it with fresh lukewarm water to rinse out the soap and then drain again. I would then fold the quikt top up and press out as much of the water as possible and then dry the top.
If the prints are COMPLETELY gone, I would put it into the dryer until it is just slightly damp and then spread out to completely dry. If there are still faint mud prints on the top, I would air dry on the line because heat from the dryer will set the stains.