You can block all texts yourself via your on-line MyVerizon account, assuming you're the Account Owner and logged in as such. Once logged in, look to the left under My Device and click the blue Change Features. Choose the appropriate line if appropriate and click Next. Scroll to the bottom of the page and click the blue Block messaging, data & other services. Put a check next to each of the three messaging options at the top of the page, then click Continue. You'll get a pop-up screen to review your changes; if all looks ok, click the red OK (you may need to scroll down a bit to see it, use the slider next to the pop-up box).
