Hello RUSSELL.A23. That's a great question. What is the make/model of your phone? Do you use Verizon Messages + online via desktop computer or via the app on your phone? Also, are you having any trouble with the app? Check out this great link: Verizon Messages FAQs | Verizon Wireless Share details.
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are you talking about the red icon marked messages? If you are you can go into settings/applications/applications manager/ and go down to message+ (the red one) tap on that and you can disable it