Black iron pipe will rust. If you clean the rust off of black iron pipe, it will rust again. Clean it again and it will "beat you to a pulp" proving to you that it can rust faster than you can clean it off....
From a "corrosion control perspective" a light coat of surface rust will prevent "excessive rust damage from occurring". If it bothers you, buy a can of "FLUID FILM" and spray the pipe, wipe off any places where it's dripping, the next day with an old rag. Wear OLD clothing and eye safety glasses to spray the pipe. You WILL wear more than the pipe when you're finished....
You can buy it at Lowe's (in the automotive section), at AutoZone or on Amazon:
https://www.amazon.com/Fluid-Film-AS...1FSYYB8O&psc=1