The heatsink is held in place with a bent metal spring clip that latches to the main board in two places on either side of the compute module. The green board is pictured here, but the blue board works functionally the same way.

One side of the clip (highlighted here in orange) is simpler. This end is designed to be removed first.

The other end of the clip (highlighted here in red) has an extra bend which helps secure it. This end can only be removed after the other end has already been released.

Both ends of the clip are retained by a pair of slots in the main board. Each pair has an outer short slot and an inner long slot.

Look at the board edge-on while working with the clip so you can see how the bent ends are positioned relative to the top and bottom sides of the board.

Starting with the simple side (the side without the extra bend), push the clip down through the board until it releases, then allow the clip to compress so the end can be raised up through the longer slot.

Now that the clip can move freely, rotate it upwards by 90-degrees, so it's perpendicular to the board. Move the other end of the clip down through the board, then sideways so the end can be raised up through the longer slot.

Now that the clip is entirely free from the main board, put it aside somewhere safe.