Currently TeamSpeak appears to use signal to volume level to determine whether or not to activate the microphone. This causes problems for various gamers as their mics are too sensitive to their keyboards -- I myself suffer from this problem.

My suggestion, is to take advantage of voice detection algorithms (& potentially machine learning/potentially implemented via machine learning) in the TeamSpeak desktop software. TeamSpeak would then have 3 voice activation modes:
- Volume
- Voice Detection
- Volume + Voice Detection

Volume is the existing mode.
Voice detection mode would trigger the mic by listening for audio input, that well, resembles a person talking.
Voice detection + volume mode would trigger the mic by listening for audio input, that resembles a person talking, and that is of sufficient volume -- this is to prevent TeamSpeak from feeling like it's snooping on your SO's conversation on the other side of the room.

Voice detection may add an additional delay to the transmission of speech -- the amount largely depends on the algorithm used, and how much audio input it needs before it can determine if the sound clip contains speech. I think the overall benefit of eliminating background noise during periods of vocal silence, and potentially providing an even easier setup for users, would be well worth it though.

This may be a starting point for an implementation:
https://dsp.stackexchange.com/a/2629

Thanks for reading