You do need to drain their marsh before the Corp of Engineers finds it and delineates it as a wetland. Once that happens, you are fucked and it's as if the land never belonged to you. (But you will still pay property taxes on it).

If you can find their den or if any of the tunnels they are using are sealed you can drive a four wheeler or any gasoline engine nearby and run a piece of metal dryer vent hose or any heat resistant hose from the exhaust to the hole and just leave the machine running. I've rid my yard of moles with a lawnmower doing this. As you know, carbon monoxide is the silent killer.