Almost everyone wants to delete received text messages on their iPhone. Is it because you want to keep the Messages app tidy or because you want to keep messages private.
Why Text Messages Are Not Really Deleted
Text messages hang around after you "delete" them because of the way the iPhone deletes data. When you "delete" certain types of items from iPhone, they aren't actually deleted.
Instead, they are marked for removal by the operating system and hidden so that they appear lost. But they're still on the line. These files, like text messages, are not actually deleted until you sync your iPhone with iTunes.
How to permanently delete text messages on iPhone
Step 1. Install iOS Private Data Eraser on your computer
Install and launch the program on your computer. Connect iPhone with your computer via USB cable. After that, select "Private Data Eraser" to delete text messages on iPhone permanently.
Step 2. Scan existing and deleted text messages on your iPhone
In this program, click "Start Scan", and then the program starts scanning for text messages on your iPhone. Wait while the program scans your iPhone.
Step 3. Delete messages permanently on iPhone
When the scan is complete, you can check "Messages" and "Message Attachments" to see all the messages that you will permanently delete. Click "Erase from Device" to delete text messages from your iPhone completely.
The program will ask you to confirm your operation by entering the word "delete". Do it only if you are sure of it. Then click "Delete now" to continue.
After the process is complete, you will see a window as follows. Then the messages (deleted or the ones you have selected) will be permanently deleted from your iPhone.
Related - How to Delete Iphone Photos Permanently
Delete text messages on your iPhone manually
Tap the Messages app > hit Edit > hit the reading circle, then you can delete the entire conversation from your iPhone. Or tap to open a conversation > tap any message > press 'More'. And then you can delete any message in this conversation that you need.