If you miss something important it's no big deal because muting a conversation doesn't delete any messages. Simply search the conversation's subject line and it'll retrieve every message in the chain (including ones that have been sent since you muted it). And if you want to opt back in to the chain at any time, it's easy: just follow the same steps above that you did to mute, only this time you'll obviously select Unmute.
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Joe McGauley is a senior writer for Thrillist and frequent user of the mute button.