Unlike voice, there's no way to block specific SMS messages or sending parties. You can disable SMS completely for one Twilio number, but you cannot selectively reject messages.
If you would like to block all SMS, you can remove the URL from the SMS section of your phone number settings in the console. To disable incoming SMS on all Twilio phone numbers associated with a Messaging Service, simply uncheck the "Process Inbound Messages" checkbox under Inbound Settings section on the configuration page.
Or Simply click on this link here > Select The Phone Number > Scroll to Messaging to "A Message Comes In" > Remove the WebHook URL.
After doing this you will not be charged for, nor will you receive, SMS to your Twilio number(s).
We understand that many customers are worried about abuse, so if your project is ever subject to abuse you can contact us and we will work with you to resolve the issue as soon as possible.