They're not really grease nipples. They're just vents. If you look carefully, you'll see that the check valve is missing. There's only a hole going all the way through.
When you think about it, it makes sense. The bearings are sealed and can't be greased.
I talked to an engineer who worked for a major manufacturer years ago about why they do this. He told me that when they went to sealed bearings, they eliminated the grease fittings. The customers and dealers had a hissy about how to grease the deck bearings. They explained that it was no longer necessary but fell on deaf ears. So they installed these vents to allow any water that go into the sleeve to vent out. (At least that was the theory). They don't recommend pumping grease into this fitting as it will eventually dry out and attract water.
As for your condition, you need to close the opening to prevent water or dirt from entering.