FOLLOW UP. There is an even easier method to get the battery compartment open. You don't need a butter knife at all. Instead, use the same small flathead screwdriver to press down on the tabs along to right and left sides. Using this method, it took me all of 20 seconds to remove the compartment.
Just a note to make things a little easier: when using the butter knife, you want to depress the two tabs near the FRONT of the battery holder, on both sides (look at the picture). Those tabs stick out slightly further than the opening, which is obviously what prevents you from puling the battery holder out. Depressing the tab will make it more or less even with the opening, allowing you to pull it past the opening.
@Endrju I don't understand why you do "not believe" in the rechargeable batteries on Amazon. I purchased mine on Amazon, and the new battery actually lasted twice as long as the original Logitech battery. Your solution requires a lot more work than simply replacing the battery.