Open the Messages app
Swipe left on the conversation or message thread
Tap Delete
Confirm the deletion if prompted
To delete individual messages, open the conversation
Touch and hold the message
Tap More
Select the messages you want to remove
Tap the trash icon
Tap Delete Message
To delete multiple conversations, open Messages
Tap Edit or Filters
Select the conversations
Tap Delete
Tap Delete again to confirm
Turn off Messages in iCloud if you do not want deleted texts to sync across devices
Go to Settings
Tap your Apple ID name
Tap iCloud
Tap Messages
Turn off Use on this iPhone
Remove old backups that may contain the texts
Go to Settings
Tap your Apple ID name
Tap iCloud
Tap iCloud Backup
Delete old backups if needed
Erase the iPhone if you want to remove all data
Go to Settings
Tap General
Tap Transfer or Reset iPhone
Tap Erase All Content and Settings
Set up the iPhone as new if you want the most complete removal
Use secure data erasure tools only if available and appropriate for your device
Note that deleted texts may still exist in backups, synced devices, or the recipient’s phone