Driveshaft Mercury Part
The driveshaft mercury part in the stern drive lower unit is the plastic, splined piece that slips over the driveshaft. It also has a rubber seal that installs on top of it. When you grease the splines, you'll probably be spreading some of it over the plastic piece as well and if you don't clean that off, it can cause a hydraulic lock where the driveshaft enters the crankshaft snout. That can force the crankshaft upwards on the bearings, which will do bad things to them.
If your lower unit isn't pumping water, you might try turning the flywheel counter-clockwise to see if that makes a difference (it should). You can also spread a little more anti-corrosion grease in the center and around the rubber "bellows" seal, but make sure you don't put too much on the splines above that.
These products are manufactured by Sterndrive Engineering, Inc and not the Brunswick Corporation. The MerCruiser(r); Alpha One(r); R; MR; Gen II(r); Bravo One(r); Bravo Two(r); and Bravo Three(r) are registered trademarks of the Brunswick Corporation.