Some soaps and pump action liquid hand cleaners contain ingredients that can create black stains if they get into the washing machine. If the stains or black marks look worst when the garment is held up to the light? then hand soaps may be the problem. This may occur if the hands are washed but not thoroughly rinsed, some of the hand soap ends up embedded into the towel and then circulates inside the wash when the towel is in your washer. It creates a chemical reaction which attracts dirt during washing!
Make sure every one rinses their hands thoroughly before drying them on a towel