I really don't understand the outrage of dumping some GRAY water. Of course, use common sense, not near water, not near other people or civilization, use biodegradable soap and make sure there aren't any "chunks" from your dinner.
Tenters don't hesitate to dump their dish water into the nearest bush, or put out a campfire with it. We admit to responsibly dumping a few gallons here or there. On a few occasions we have also "dribbled" slowly through the garden hose attachment while driving down a dirt forest road. That way it is truly dispersed and low impact. Don't see the harm in that. There are way worse nasty fluids and particles that come off our vehicles and pollute the environment. A little dirty water isn't gonna do much. We also don't have a black tank that makes us need an official dumpstation.
Plus, I'm sure the flora doesn't really mind the extra water, especially in the desert. In terms of a smell attracting wildlife, if you are in the boonies that shouldn't really matter that much. Won't smell for long and you will be gone. There are many worse stinks in nature that get checked out.