How to Delete Text Message from iPhone
Delete an Entire Conversation
Tap the Messages app on your iPhone home screen. In iOS 7 or later, Tap the Edit option on the top left. Tap the little red circle on the left side of a conversion and tap the Delete option on the right side. In iOS 6 or earlier, find the conversion you want to delete, swipe left to right and tap the Delete option.
Delete Single Text Messages within a conversion
Tap the Messages app on your iPhone. Find and open a conversation within which you want to delete SMS. In iOS 7 or later, tap and hold on a message until a pop-up appear. Tap More. In iOS 6 or lower, tap the Edit button on the top right. And then check unwanted single text messages by tapping the circle on the left side of each text message and tap the trash bin at the bottom to delete them from iPhone.