In that image the heatspreader looks like a single sheet of folded metal. It would be held onto the RAM by its shape and fixed in place by the adhesive properties of the thermal interface material below.
I've removed one similar and had to bend the heatspreader a little to get it to move. Applying heat may help loosen the hold of the thermal material, but this is only hearsay.
On other modules where i was less concerned about the RAM surviving i applied plenty of force and pulled the clamshell style heatspreader up and away from the dimm. I did not damage the RAM in either instance, but the heat pads couldnt be reused where the heatspreader was not bent, and bending the heatspreader back into shape left obvious signs that it had been warped and tore the thermal pads/adhesive.
I didn't try sliding the heatspreader sideways.
Proceed with caution, of the 60+ DDR3 modules where i have removed the heatspreader none were damaged, but my understanding is that manufacturers are using much stronger bonds between the chips and heatspreader now. As i said in my previous post, chips have been known to come away with the heatspreader so it might be worthwhile adding heat to soften any bond if present, as well as using a spudger or plastic card to pry the metal away from the dimm.
Obviously, if there is a screw and you miss it then you are screwed. Pun intended.
But looking at the image that doesn't appear to be the case. None of the heatsinks i have removed have had screws holding them to the board. I do not know if that is common or simply the case with the heatspreaders I removed.