Remove the Phillips screw and gently pry the metal plate from the Joy-Con (a pair of tweezers might help). Be sure to hold the buckle lock in place so the spring does not fly out.

The buckle lock is different for the left and right Joy-Cons. Before you remove the buckle lock, identify the part that you will be replacing it with and make sure it matches the orientation of the original. Pay particular attention to which side is tapered and which side is straight.

Remove the buckle lock, being careful to keep the spring inside from flying out.