I have/had lots of pieces of machinery with holes drilled for the same purpose, they allow one to keep the protective shield in place, while making greasing still possible.

I have several holes the same size drilled in those big awkward CVJ's on my Bush Hog mower.  It works even better if I use an adapter I made for another purpose to help get in position, and allow the use of a power greaser that might lock up inside the assembly and be difficult to remove.

I made this a long time ago, so long I forgot the original purpose.  All it involves is a 3" 1/8 galvanized nipple with a collar.  I screwed a zerc on the collar, a grease fitting on the other end.  Makes a short tube I can stick through all the mess easily, then plug the battery powered Lincoln into the zerc.  I can control the angle better into the zerc on the PTO universal joint, because I can move the adapter easier than the whole hose and zerc.  The 1/8 nipple is smaller diameter than the hose and greaser end, so I can see the process better.  Sometimes I clamp a small vise grip to make it easier to hold, as when it gets greasy sometimes that is difficult.

If the power greaser locks on the zerc, it is easier to remove from the adapter.

(EDIT) I remember now why I made this.  It was used and still used to grease throw out bearings on IH tractor clutches.  This zerk was often deep into the tractor, and I previously had problems reaching in and making sure it was taking grease.  After I made the adapter, I could use a light and assure I was straight on the zerk. 

In fact, on my 856D we used to have, we even added an extension to the original zerk, which made it much easier to add those two or so pumps each year that were required.  Our 856 had belly fuel tanks, and they almost covered the zerc opening, making it even more difficult to grease, hence the adapter.  The procedure was to lay a mirror on the belly tank in order to see the zerc illuminated by a light in the bell housing. (This post is bringing back a lot of memories!)