Mute Button next to the Pause Button to Mute the Sound when recording. To Permanently Mute the Sound, would be to uninstall Jing. Restart the Computer and reinstall Jing. When starting Jing up, after signing in, you can configure Jing for No Microphone Use.
I am not aware of a setting to disable this. You will only record a message if you tap on the mic, and you will see the recording. Just tap on the to close and delete the audio message. You actually have to hold the icon to start the recording, and once you have typed in the message box, the mic is gone.