Difficult to see from the photos, but could this be some kind of push-pin mechanism where the sides of the pins compress as they are squeezed through the hole and then expand to lock them in place? In that case, you would have to squeeze the sides of the pin together with pliers while simultaneously pushing it through the hole from above to release it.

Poke screwdriver in the top hole on the tight side, lever, pull fan up a bit.
Should get 1. 3 to go.

Thanks for the advice guys. I managed to pry it off. The pins at the top don't seem to do anything much, maybe you need a special tool or something. Using a screwdriver (tried various sizes) didn't do much. Eventually, poking at the grips and applying a good amount of force with a screwdriver in one hand and trying to pull the cooler up at the same time was quite challenging all the while trying not to let the screwdriver slip and stab yourself in hand.

Eventually there was some movement and I was able to lift the cooler. Once the first grip was loose, the others starting to let go as well.

We now have a clean heatsink + cooler that can be put back to work... 😀