Is there no problem dumping grey water on the ground in campgrounds? My grey water doesn't have food particles or grease. It's only hand soap, or dishwashing soap.
When I'm dry camping for days I'll empty the gray onto the ground through a designated garden hose so as to not get any more "black" than necessary. It also enables me to run it 25 feet away from the camper to an area where it won't bother anyone.
It's kind of a last resort and I'd never dream of doing it in a campground with facilities nearby. I also try to use biodegradable soap when I think I may be dumping onto the ground.