How do you retrieve messenger text messages?

Your question refers to Messenger. Do you mean the Facebook Messenger app? If so, that is something you would have to ask Facebook. If you are referring to Messages (see the difference), if you are not using iCloud Messages, if you have a backup of the iPhone when the message was still on the iPhone, you can restore to that backup, unless you have made a backup of the iPhone since you deleted the message. It is iCloud Messages that you cannot restore deleted messages from.

Like I said, if you were using iCloud Messages, you cannot recover. You never responded if you were using the iPhone Messages app or Facebook Messenger. Two different things.

Only from a backup. Restore it to a spare device, then sync messages through iCloud. If you are OK with these messages in PDF you can use some app like iMazing to access them, backup browsing works in trial: https://imazing.com/guides/how-to-save-iphone-text-messages-sms-and-imessages-to-your-computer