Scouts should know how to dispose of water which has been used for cleaning dishes, which is also known as gray water. One issue with gray water is the little bits of food left in it. These bits of food are covered in soap residue. If animals find and consume these bits of soapy food, they might become sick.
One easy way to strain dishwater is to use a plastic grocery bag. You might have one you used to bring some food to camp. Poke some small holes in the bottom. Then throw in a several large handfuls of leaves or needles. Put a couple of sturdy sticks in the ground and prop the bag open on them. Slowly pour in the dishwater. The bits of food will be caught in the leaves and the water will drain out the bottom. Then just tie up the bag and throw it in your trash.
This method can be used with smaller amounts of dishwater. Just make sure it is not steaming hot when you pour it in the bag. Also remember to do this at least 75 steps away from creeks, streams, lakes, and other open water. Detergent is hazardous to fish and other animals living in the water.