It is much easier to insert and remove the muff body clips by rotating them 90°. The plastic stud underneath is oval in shape and is indicated in green on the image.

Remove the pad by inserting a large flathead screwdriver or butter knife just underneath the plastic backing plate of the padding and continuing all the way through to the muff shell. Then twist forcefully, and the underlying plastic should pop off. Using a finger is nearly impossible on the first attempt, but works on subsequent attempts.

Now it's free! But be careful to not twist or yank the cable.