After the first rain or two, the gravel and pipes etc should be washed off, and the water should run clear, with little noticeable color. The color is obviously soil, and if it keeps up its because theres an erosion problem somewhere in your system.
How you cover the system depends on what it needs to do. Topsoiling over it will prevent surface water from getting into the pipe, but will allow groundwater into the pipe. Fully backfilling with gravel will allow surface and groundwater into the pipe.
A swale is open ended, and therefore doesn’t impound water. A depression is closed, and will impound water. Since you mentioned you have a swale, you probably dont need to collect surface water, therefore topsoilling over it will be okay.