If you have customers that have requested you not to text them, or are receiving spam texts, you have the ability to block them from their customer profile on the Chats page.
When you block a customer, they will no longer receive messages, even if there were scheduled messages previously. They do not receive any sort of notification after they have been blocked. They will also disappear from the chats list unless purposefully searched for.
If they were to message your team once blocked, you will not receive a notification for the message. You can, however, search for by name or number for the customer's chat to check for any new messages.