Incoming messages are free, so we do not have a 'turn off' option. But here's a way that they won't bother you for a long while.
The idea is to use the Vacation Reply option in our Auto Responder.
When you choose the End Date, use the double arrows on the right-hand side (blue box in image below) to set your year far into the future. At the moment, the end date would be 2035.
The auto responder settings work per phone number. This enables each phone number to have unique settings if desired.
NOTE: This option costs the standard 1 credit per 160 characters each time it is sent.
REMEMBER: Incoming texts are free; outgoing are not. So we recommend setting your auto response to once a day.
This article has the full walkthrough for using our auto responder: