How do I dispose of a dead animal carc?

I found a dead coyote in my grandma's front yard, under some brush. I looks like it hasn't been there for very long, since it still looks partially intact. My grandma wants it cleaned up asap, but I suggested leaving it for a few days to let the maggots clean it up first, that way I would only have to pick up hair, bone, and whatever else is left. Right now it is absolutely covered in maggots, so it's already in the process of decomposing. What is the best choice of action for taking care of this problem? Should I wait for the maggots to clean it up first?