On Linux [1], with a pair of Bluetooth headphones connected and configured to use a unidirectional audio codec such as A2DP, connecting to a ThinLinc session with audio redirection enabled switches to a low-bitrate bidirectional audio codec. When ThinLinc is closed, the codec is switched back to the unidirectional high-bitrate codec. This is presumably related to the fact that the ThinLinc client "uses" the microphone at all times (and not when the microphone is actually needed inside the session). Note that you can still switch back to the unidirectional codec on the client machine while ThinLinc is running. [1] Fedora 40 machine running GNOME.
I have not tested the behavior on other platforms or distributions.