I removed just a cover yesterday. The cover may be aluminum or vinyl. Undoubtedly, it has flanges to the left and right that are nailed to the subsurface (old siding). The J-strip is nailed to the top of the flanges. If you can cut between the cover and the J-strip, you might be able to remove the cover and then caulk it back in place. If not, you might as cut, grab, cuss and remove the siding from the J-strip. I am planning to repair the wounds I made (there were two pipe and covers) by replacing the siding. The replacement is possible because new pipe was installed and is proud of the top layer of siding.