TeamViewer - local audio is disabled when connected to remote
Solution 1:
I am one of several people who had the same issue. Here is a fix from the page Bluetooth Sound lost after connecting to a client (at TeamViewer.com).
Go to TeamViewer's Main screen and navigate to "Extras" → "Options" → "Audio Conferencing" → "Voice Playback". Change it to any device other than the one you are using for local audio.