After you unscrew the 4 screws under the battery cover, the sides can then be popped out as they simply snap into place.
I just stuck my fingernails in the crack between the chrome side and the phone and pulled out and one end popped off. From there just run your fingernails up the other side and each segment will pop off.
After I put it back together it seemed to squeak less. Maybe it just needed to be adjusted? I would have to estimate that it is a 90% improvement from before I took it apart. I didnt add any glue or cushions, just simply snapped it back together. Very strange but I'm not complaining