I've encountered a problem pulling my drip rail mouldings. Infact, I broke one side trying to get it off. I have noticed that they were stuck on with double sided trim tape.
I had pulled a set at the junkyard when there happened to be a wagon present. They came right off in my hands with a just a gentle twisting motion.
The ones on my car were a bear. I made a makeshift tool using a flat piece of metal bent in a loop with a narrowed edge that caught underneath the moulding. You then were able to pry upwards and it helped twist the moulding off. However, it had to be done a section at a time, or else you can easily destroy them. I learned the hard way first time around.
They are very soft metal, so caution is advised.