In Gmail, email threads can be muted.
How can they be muted in the Google Inbox mobile web interface?
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In the Inbox web UI there is no menu option for Mute, but you can use the M key. Sorry I didn't see the "mobile" part of the question before I answered.
There is no way to Mute in the mobile app AFAIK at this time.
Hitting ? will display the keyboard shortcuts and allow you to enable / disable them.