The longer you wait to clean up, the harder it becomes because food congeals and sticks to the pot. Waste no time cleaning up after you finish dining.Washing dishes in the backcountry does not require soap. The Leave No Trace method for dish washing involves hot water and a scrubbing sponge.
After dining, put some water in your dirty pot.
Light your stove, put the pot on the stove and heat the water until hot but not scalding.
Remove the pot from the stove. Scrub it with a sponge (or try gravel and sand) until all of the solid matter is removed. Wash your dishes and utensils in this water too. If you must use soap, make sure it is biodegradable.
Dispose of your gray water by either straining or drinking.
Straining: Pour the gray water through a bandana, coffee filter, or even your fingers to catch all food particles. Pack out all of these scraps with your garbage. Scatter the remaining waste water in the bushes well away frm camp and 200 feet from water. If you are in the same site for several nights, consider digging a sump hole into which you may deposit the water.
Drinking: Using the human garbage disposal method saves you from having to carry smelly food scraps and a dirty strainer (bandana or such). Simply drink the water that you used to clean your pot and dishes. I have practiced this method on occasion and it is really not bad. Think of it as an after dinner soup.