It's not illegal in most places to pour greywater in/on the ground- but it IS illegal to create a nuisance by doing so. Grease and food particles do attract vermin, plus they smell nasty.
Here's how we were advised by a forest service employee to dispose of greywater in the woods etc.:
Choose a location at least a hundred feet from streams/lakes. Dig a hole a foot or so deep, place greywater drainhose in it, and drain slowly enough that the hole doesn't overtop. Backfill and tamp down the hole when finished.
We always go a step further and dump a couple of buckets of cold ashes from the ever-present fire ring in the hole while dumping- natural filtration/odor control!
If allowed, "burning off" the grease/food residue before backfilling is better yet.