Per the EPA, you can let the pit mud dry on a non-permeable surface with any run-off allowed to go to a sewer drain, and once it's dry you can dispose of it in your dumpster or landfill. I used to shovel the mud onto the bay floor and let it dry overnight and wheel it to the dumpster the next day, but the smell was too bad.
We had one pit filling up twice as fast as the rest, so I covered the whole grate with steel, with only a 4" hole cut in the center. Whenever there's a heavy mess I place a pail over the hole and rinse everything onto the steel, then move the pail and allow the water to drain. After about 5 minutes I can pick up almost all the mud quickly and easily with a shovel, which I put straight into the dumpster.