The opposite side you are referring to is the fixed cup. If you can see it and it looks OK, just clean it as best you can and leave it be. If you REALLY want to take it out, I would suggest taking it to a bike shop to have it removed (IMO). The pitting to look for would be on the bearing cup(the part in the upper left), more specifically you want to look at the bearing race, which is the shiny smooth part the that the bearings fit into. Pitting refers to just that, "pits" in the surface of the race or bearings. From what I can see the cup looks OK. I cant tell if your bearings are pitted or just dirty in the above photo.

My recommendation would be to clean everything really well and put it back together. If you clean the bearings and they still look rough, I would replace them. Your LBS should have replacements, just take in the old ones for comparison. Bearings are cheap.