Mute Gmail Threads

2.Touch and hold a conversation thread (or touch the thread's icon/picture) to add a checkmark to it, and then tap Archive .

The thread is now archived.

Mute Gmail Threads

If registered on a mailing list, there will be threads with always-continuing conversations. For long threads that are not important, mute the threads and they will no longer appear in the inbox. When new mail arrives that includes user's address as a recipient or in Cc, mail will again appear in the inbox.