Pipe clamp - cleaning black iron

I have to clamp a ~50" workpiece so I broke down and bought my first pipe clamps. It sounds like black iron pipe was the way to go, so I bought that. I used mineral spirits to clean the pipe of excess sticky residue, but it looks like I'm beginning to strip off the black coating completely in some areas. I don't know how, I only had paper towels. The worst part is, the pipe still transfers stuff to my hands.

This is probably basic, but am I supposed to strip the black off or did I somehow overdo it? If I overdid it, what should I have done differently? Is there a way to salvage this or do I need to get new pipe? I've got oil-based primer, oil-based enamel, and high heat black spraypaint. All rustoleum if it makes a difference.

(.-.)

Pipe clamp - cleaning black iron