Yes your grease problem could very well be coming from your transmission case or the lower oil seal on the crankshaft of your engine. The best thing to do right now is clean off as much of the oil problem as you can using Gunk Engine Brite or equivalent engine degreaser. Install your belt and give your yard a mow. Check it frequently until you find where your problem is originating.
Scott Deaver: B&S Authorized Master Service Technician, June 2005