05 grizzly 660 mud in my tranny

So after a nice hard day of mudding just when I got done my engine temp light came on and coolant was everywhere. When I went to run more coolant in it the next day to find the leak I noticed a crap ton of dirt dust coming out the back end. What I found is chunks of dirt in what I assume is some sort of intake for the tranny that comes out under the rear rack. I took that whole piece out and looked into the tranny to find more dried up mud. It still runs fine I don’t hear any funny noises but the dirt dust keeps flying. How big of a problem is this aND is there a safe way to try and get that mud out