Firmly push the small tab on the top of the clip toward the body of the LINK reader. While holding the tab in that position, slide the clip upward to remove it. The first time you do this, it will be stiff. The clip is designed to be sturdy to avoid breakage and provide a secure fit on your belt.
To replace the clip, line up the sides of the clip with the grooves on the reader. Slide the clip downward. Make sure you hear a "click" and the sides of the clip are flush with the body of the reader. Then you'll know the clip is once more secure.