New territory for me, but im guessing you would first inspect the backplate to see if there are any obvious holes where something has pushed through, if so turn the back plate so those holes are not where they used to be, then dont tighten the cooler as much as you did before.
Which reminds me, I've read that over tightening those screws can cause board warp with then affects your memory... but I cant remember if that is type of main board specific or not... the solution to this is by loosening those screws a little and seeing if that helps. You might as well try that a few times before taking it off.
When it is off, even if there is no obvious damage to the back plate you could always try your old cooler as well, just to see