I just successfully removed the faceplate on my Frigidaire side-by-side refrigerator and wanted to share how I did it in hopes that it may help someone else. My model number is FRS64EW0, but it sounds like most of the dispenser faceplates are the same.
Step 1: Remove the tray at the bottom. This can be tough because it feels like it's going to break as it's being removed. However, once removed, the imprinted message says that the piece is dishwasher safe. I assume that this means it should be removed periodically for cleaning. I removed this by wedging a wide, sharp screwdriver between the tray and the refrigerator door. I worked first, prying on the side away from the door handle and then the side the door handle is on. It does take a little more pressure than I was comfortable applying to remove this piece.
Step 2: Remove the three screws that are exposed by the removal of the catch tray. These are at the bottom of the faceplate.
Step 3: Slide the faceplate up to remove it. There are no more screws. I had to wedge a putty knife in the upper area between the faceplate and the door to assist me in sliding this up, but it should slide up on its own.
That's it, now the innards of the dispenser are exposed and any furthar disassembly is obvious.
I hope this helps.