To stop receiving or getting notified of new messages from a customer, you can block the conversation by clicking on Block conversation under the conversation options menu. 🙅🏼♀️
By blocking a conversation, the customer will not be notified of the blocked conversation and will still be able to message you as normal.
To unblock a conversation, you can access these under blocked conversations from the left hand side menu, select the conversation, and click on Unblock conversation under the conversation options menu.