If you are cooking over a fire, you can cheat.

While the item is still dirty, drop in a bit of wood ash and enough clean water to make a paste, scrubbing with a bit of paper towl or rag. The lye in the ash will mix with any fat in there to form soap. Scrape slurry out, rinse with fresh water.

Otherwise, while things are still freshly dirty, wipe out with paper towel or TP, and as little clean water is possible. Pour it into a seperate container. That goes into the latrine. If it has a chance to dry, or worse, burn on, a bit of green scrubby works wonders so long as you aren't packing anything teflon (which should never need it in the first place).