You could also use a hot glue gun and put a drop of glue into the hole of the buzzer. You'd be amazed at how quiet it becomes.

It is non-permanent and you can pull the glue off when you want the sound again.

big thanks for mods:
"happy wife, happy life" 

I'd be concerned if the screw backed up. A piece of tape over the hole should do the trick?

I've not heard a beep out of mine (with the M3 screw in the hole).  And yes, I'm thinking about popping the lid an securing the screw in place with some tape.

I have S3 firmware from September 2014, but that just reduces the beeping when set to false. When the internet connection drops, it still beeps. Is there another setting I should be looking at?

If it beeps at night and wakes my family, the S3 will be out of the house the next morning. Such a bad design. Thanks!