How to Delete Text Messages Permanently on the iPhone
The iPhone's Messages application stores all text messages sent from and received by your iPhone. At times, you may want to delete a specific message from the Messages application. You can delete specific messages directly from the application. This delete feature allows you to remove only single messages; the iPhone does not allow you to remove multiple text messages simultaneously.
Tap the "Messages" icon on your iPhone.
Tap the "Edit" button in the upper left corner of the Messages application.
Tap the deletion icon (a red circle) located to the left of the individual text message you want to delete.
Tap the "Delete" button to permanently delete the text message from your iPhone.