Alls that needs to happen, is to pump a couple thousand gallons through the ship's filtering system and test the water that comes out of the other end. That should take, what? A day?!?
We'er seperating water from oil. That ain't rocket science. Oilfield hands do it everyday with heater-treaters and seperators designed for that exact purpose.
It's highly possible that the ship uses oil/gas/water seperators to clean the water.