A club discussion has become a long stream of acknowledgements. You still want to keep the conversation, but do not need every reply in the inbox. Gmail’s Mute acts on that thread; it is a different choice from blocking a person or unsubscribing from a mailing list.
Choose the thread deliberately
On Gmail for a computer, select the message and use More, then Mute. Replies normally skip the inbox and remain archived. This does not delete the conversation. Before using it on an important discussion, decide when you will check for updates and keep a reminder outside the thread if necessary.
For example, muting casual acknowledgements after an agreed meeting may be convenient. A thread carrying the final room change needs a different plan: arrange a check rather than assuming that quiet means no new information.
Know the exceptions
Muted messages can still reach the inbox when sent only to you, sent to your Google Group, or when someone adds you to To or Cc. Mute therefore is not a promise that a conversation will never appear again. Read the new message before treating its appearance as a broken setting.
Find it and reverse the choice
Search is:muted, select the conversation and use More, Unmute when you want to follow it again. Check the subject and most recent messages so you change the intended thread. Keep any attachment you still need. Finding the thread is more useful than repeatedly looking only in the inbox.