Open the Messages app
Delete the conversation thread
Tap Edit or Filters, then select the conversation and delete it
Go to Settings
Tap Messages
Turn off Messages in iCloud if you do not want messages to sync back
Go to Settings
Tap your Apple ID name
Tap iCloud
Tap Messages
Turn off sync if enabled
Go to Settings
Tap General
Tap iPhone Storage
Find Messages and delete large attachments if needed
Clear recently deleted items in the Photos app if messages contain shared media
Restart the iPhone
Sign out of iMessage on other Apple devices if messages keep reappearing
Erase the iPhone and set it up as new if you want all message data removed completely