It is most probably because the straps are filled with some kind of foam rubber. The tiny pockets of air in foam rubber are not necessarily completely sealed, but they may take some time to ventilate and adapt to a surrounding change of pressure.
If you have a piece of foam rubber and rapidly decrease the surrounding air pressure, the foam will initially expand, since it takes some time for the trapped air to escape, allowing the internal pressure in the foam to adapt to the external pressure and the foam to go back to its original shape.
When you are landing, the air pressure in the cabin increases and the remaining lower pressure within the foam causes it to collapse and stiffen. Also this way around, it will take some time for the foam to 'suck up' air and align the internal and external pressure.