To repair using the repair kit hold the repair kit and click the lever or gate lock.
The repair kit is found at fixed locations on the Guild Hall map during battle. There are two on the map, enough for each of the Trebuchet on the map. They can both be picked up and moved by either team and used to repair the trebuchet which allows them to fire.
Often a team GvGing on these maps will retrieve the repair kit closest to the trebuchet pointing at their base and stash it in their base to prevent it being easily used to repair the trebuchet against them.
The repair kits appear on the maps which give the highest advantage to the "home side". They spawn at Equipment Stations if the side defending on the map takes the point. It can be used to repair broken gates to the central fort to slow the attacking forces.