The amount of peppering is genetic. Heavy peppering is considered undesirable by most breeders and hobbyists and so those fish are usually culled or sold to pet stores.
However, pepper will lighten and darken just like the bars on a regular, non-pigeon discus. If you have a fish with heavy peppering, lightening up the tank will help to lighten the appearance of the pepper that it has.
It is not always related to stress, as I said in my previous post, but stress can bring it out and make it more noticeable, just like regular discus' bars.