Follow along with the video below to see how to install our site as a web app on your home screen.
Note: This feature may not be available in some browsers.
When you select Text Message, select the contact that you want to delete the conversation (at this point, you should see chat bubbles, the actual text). Then click the menu button and there should be a "Delete" button. This will delete all the messages on a "per contact" basis, rather than just wiping all messages with everyone.
To delete all of it, go back to the page that lists all your text contacts, click the menu button, click the button "Select multiple", and now at the bottom, it should have 2 buttons, Delete or Cancel.