In Gmail, email threads can be muted.
How can they be muted in the Google Inbox mobile web interface?
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.