Mute a specific conversation on an Apple Watch of a Family member without their own iPhone

I want to mute a specific conversation on an Apple Watch of a Family member who does not have their own iPhone. (My AppleID and iPhone was used to set up their watch with their associated AppleId). ## Related: * [how to customize watch to silence certain texts - Apple Community](https://discussions.apple.com/thread/250936142?sortBy=best) - This requires the family member to have their own iPhone, which is not my case. * https://apple.stackexchange.com/q/261795/329079 - It is not clear how to actually do this. Also, it probably will not help, since it looks like it is a connection with iPhone. In my particular situation we do not have 1:1 connection. How can they mute a messages thread on their watch?