retrieve deleted Text messages on iphone7 plus with a back-up on iCloud or iTunes or computer?

You can only restore deleted data including messages by restoring from either your iCloud or iTunes backup. It's a long shot, but you can try reaching out to your carrier and check if they have some SMS recovery option for your text messages.

ZaaD225 Said:

"retrieve deleted Text messages on iphone7 plus with a back-up on iCloud or iTunes or computer?: How can I retrieve deleted text messages Without any back up system in place and no computer?"

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What to Consider:

A. Restore from Today's Backup:

Restore your iPhone from a backup of it that contains these messages, and you could recover them.

B. Check Messages App:

If messages was enabled on your iPhone along with your Apple computer, then check and see if the Messages app is enabled on your Mac to see if it exists in it. You'd start up your Mac, not connecting to the Internet, and open the Massages app. Then proceed from there with retrieving it. Important: Be certain you do not connect to the Internet while booting up, as syncing would delete it. So, power off your router to avoid the connection.

ZaaD225 Said:

"retrieve deleted Text messages on iphone7 plus with a back-up on iCloud or iTunes or computer?: Sorry I don’t have any back up at all. Can I retrieve deleted text messages any other way? Do I need to go into a computer store for them to do it?”

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Try your Carrier’s Site:

Logging in to my carrier’s site, I can see a call log going back 90 days. Voicemail message’s calls show up, but they go away after 90 days. So, log in, seeing if they reside in there.