Thanks for the hint. It worked great for removing the covers on the body side of the hinge. To remove the tailgate covers, I gently lifted the cover end closest to the hinge and slid the cover to the left. It came right off.
Attached are some pictures of our Rugged Ridge Hi-Lift jack mount. The installation went pretty smooth except that the template for drilling the holes in the plastic hinge covers was definitely not right. I think that they photo-copied the instructions and maybe shrunk the template. Be careful with the mount's plastic knobs -- I twisted one too tight and it broke. I think that I am going to go with regular bolts and carry a wrench.