Silencing notifications on Watch

I am in a group SMS chat (not iMessage, as there are some Android members). On my iMac and iPhone I can mute notifications for the chat but cannot leave it (because it is not an iMessage chat). My Watch is set to mirror the iPhone with respect to notifications. However, whenever a new message comes in on that chat (which happens all too often during the day) my Watch still gives the audio notification (although the iPhone doesn't). I could silence all audio notifications on the Watch but that's going too far -- it would cut off audio notifications on other messages that I might want to know about. I just want to silence this one chat, and I can do so on the iPhone. Why doesn't the Watch mirror the iPhone and keep silent? (I've resorted to taking the Watch off when I get frustrated with the notifications!)

Am I overlooking something?