Alright, this is not what you think. I've searched the board. But I found mostly threads about the 360 (I have an Xbox "classic") or threads about changing the thermal compound. Changing the thermal compound is what I want to do. But I cannot get the damn plastic clamp off the heatsink!
I've enclosed a few pics. As you can see, I've lifted the black thingie and the whole thing is now basically loose. However, the orange plastic clamps won't come off. They're loose, but I can't get them off. How do I do this? It seems so easy yet I've tried for hours and I'm stuck. Totally stuck.

The heatsink...

Closeup...

Closeup from the other side... These things won't come off their hinges.