By default, when connecting AUX cable to your Xbox remote, the TV speakers will not automatically mute. 

That allows you to connect woojer strap to the Xbox remote control and still listening to the sound from the TV screen. (Make sure your TV volume is not low)

Also you can use an external BT speakers.

By using an external BT transmitter such as the one in the link below:

Pair both your headphones and “Woojer” to the BT transmitter and connect the transmitter input cable to your TV audio output. 

*Note: please remember to always set your audio source to HIGH volume.