There are some of us, in addition to myself, who actually use the web interface almost exclusively.
The "Mute this Thread" function used to be obvious - it was a button in fact - on the web interface but it's disappeared and has not been moved under the "More" button. I have an outstanding question regarding this development on the beta group and have corresponded with the original questioner off-list.
I will, however, post the answer once I have it, as many do interact with Groups.io via the web interface.
Here is a test to find out whether your mission in life is complete. If you’re alive, it isn’t.
~ Lauren Bacall