Thanks for reaching back out, peo bjorn. While you have your backup, with your messages, you wouldn't be able to just restore the messages, you'd have to restore the whole backup.
Also, before you take this step, it's a good idea to go to Settings > Your Name > iCloud and see if Messages is enabled there. If it is, your conversation will not be stored in your backup. You can read more on this here:
How to delete messages in iCloud
Also, if you deleted the entire conversation, it may not be recoverable, even when restoring a backup. The following article states "You can’t recover a deleted conversation."
Delete messages on iPhone
Have a good day.