Listen to the video, pay attention to the sound when the parts drop back to rest position.
If you were able to look inside you would likely see this:
See the whitish area that is circled? This is glue residue which is causing the noise. Take a flat bladed screw driver and pull it across this glue to scrape it off the red felt called a hammer butt square. Now test the note. If you have removed the glue residue the noise will be gone, no more "click".
Be careful not to dislodge the felt otherwise you will need to remove the action and find the felt that has come off and re-glue.