Pilot bushings are cheap (i.e. $5) and you might as well replace it while you have things apart. Getting it out is the hard part though.
Grease v. pilot bushing? The pilot bushing is a little doughnut of metal that goes into the hole at the back of the crank. If you look at the front of your transmission, the part sticking out with the gear splines on it is called the 'input shaft' The splines attach to the clutch disc. The pressure plate clamps the disc to the flywheel so that when the engine spins, the disc spins and so does your tranny. Step on the clutch pedal and you'll press on the 'pressure plate fingers' which'll release the pressure clamping down on the clutch disc.
As you might imgaine, its important to keep the input shaft perfectly centered on the crankshaft/flywheel. The way that is done is with the nub of the input shaft at the very end, the front inch or inch and a half. It actually stick into the crank shaft, thereby making sure the clutch disc is perfectly centered on the fly wheel. The hole in the crank is bigger than the nub on the input shaft. So, a 'bushing' is used to make sure everything fits just right. The purpose of the bronze oil-embedded bushing is to allow the crank to spin around the input shaft when the clutch is disengaged. If the pilot bushing is overly worn (too big) the input shaft won't be perfectly centered which can lead to a variety of problems. If the pilot bushing is too small, i.e. smashed, bent, distorted, when you step on the clutch the tranny will keep spinning, and so will your wheels-until you stall or pull the tranny again and replace the pilot bushing.
Anyhow... since it's cheap, swap it. It doesn't take long to pull and put in a new one- There are a bunch of easy ways to get it out. for example, rent a puller from Autozone. Failing that, grab a roll of TP, peel off a bunch of sheets, soak 'em in water and stuff them into the space behind the pilot bushing and keep stuffing more and more in until the bushing pops out. To put the new one back in tap it into place using a wooden dowel.
The pilot bushing is cheap and easy to find. It is a standard run of the mill small block chevy pilot bushing-
You could go the extra mile and get a 'roller bearing-bushing' for about $10 from a hotrod shop- They are very common and easy to find 'cause they are used in so many engines.
Best of luck!