The Forest Service suggests that you put a screen over the end of the hose that you use to drain your gray tank to trap the food particles and dig a hole for the water to drain into. They also ask you not tro drain it into a creek or other waterways.
I stayed in a KOA once that the owner let me drain my gray water on the campsite's lawn.
People have been draining their gray water in the forest for years and I've never seen any evidence of it.