Open the Messages app
Find the conversation containing the text messages
Swipe left on the conversation and tap Delete
Or open the conversation, tap and hold a message, then tap More
Select the messages you want to delete
Tap the trash icon
Tap Delete Message
Go to Settings
Tap Messages
Turn off Messages in iCloud if you do not want deleted messages to sync across devices
Open Settings
Tap General
Tap iPhone Storage
Tap Messages
Delete large attachments if needed
Go to Recently Deleted in Messages if available
Delete messages from Recently Deleted
Remove the conversation from all synced Apple devices
Sign out of iCloud on other devices if necessary
Erase the iPhone if you want all data permanently removed
Use a secure backup policy to avoid restoring deleted messages later