How to recover deleted messages with SMS Backup & Restore?

SMS Backup & Restore is, as the name suggests, a backup and restore app. That means it can back up existing messages (and call logs) from the phone and can recover the same from backups. To be able to recover deleted data, it needs existing backups of those messages and call logs. The backups should have been created before the deletion.
The backups created by the app are either stored on the phone or on your own chosen cloud account (Dropbox, Google Drive, OneDrive etc). The backups are never sent to the developer.
If you do not have a backup created by the app then, unfortunately, this app cannot recover deleted messages and call logs for you.

If you have an existing backup then select the Menu > Restore option in the app. The app will then guide you thru the process of selecting a backup and restore the messages and/or call logs.