Here in the Midwest the pit mud can go to the city dump when it can pass the paint strainer test (can be wet but not overly saturated that water drains out of strainer). Our mud is tested by an independent lab to make sure no heavy metals, excessive oil byproducts etc. We pay a hauler to take away and the hauler deposits on their land as long as the labs are ok.
We have also filled the mud pit with concrete to about 12" from grate. Then we scooped out the mud, put into a wheelbarrow, after the water settles to the top we poured the water out and shoveled the mud into the dumpster.