So I took a look at my PSI #PKMBCM2 TBC mandrel, which I purchased, probably close to three years ago now. This model has a metal plate on the back of the live center with two holes in it. You would need some kind of spanner wrench to unscrew it, but it looks like it is possible to pull this plate off, which should give you access to the bearings. What I would do, is mark the plate and the body of the center with lines crossing over both (say with a marker), so that when you finish greasing, you can restore the plate to its original orientation and depth (don't want too much, or too little, tension on the bearing from the plate, usually.) Then remove the plate, grease the bearing if it needs it, and restore the plate.
I've seen another version of a TBC mandrel, maybe it was a different morse taper, that I thought had one of those black plastic covers that you can usually just pop off. If you have that, then you should be able to just pull that cover off, grease the bearing, and restore the cover.
With my particular TBC mandrel, the bearing is just tight enough to have no play, which IMO is optimal. No play means that you don't have to tighten too much to take out any slop (sometimes I find that my standard 60 degree live centers have a bit of slop, and you need to tighten more to take that up.) If you have some slop, you might want to try and adjust the cover plate tighter, just to the point where you can no longer wiggle the bearing back and forth by hand. THEN mark that orientation, then remove the plate and grease.