Yeah, it really depends on what they used. If it's a petroleum based oil or grease, it'll loosen up in a typical solvent such as acetone, mineral oil, or even paint thinner (or gasoline or kerosene, but please don't use those). You can soak the whole hauberk in a bucket and slosh some of the stuff around, and rub it down with paper towels and the like. You might want to use rubber gloves for this. I had to do this once for one of mine. If you do this, use a bucket you don't mind trashing, especially since the safest way to dispose of the acetone/thinner is to let it evaporate.
The sawdust idea is a really good one. It'll still leave a small amount on the armor of course, but that will sort of disappear on its own if you wear it. Evaporation will get the remaining coating, which will be aided by movement.