After you migrate your site to the new domain, you will just need to go to WPML.org > Account > Sites (https://wpml.org/account/sites) > remove the old key (dev key) that you were using on the other domain, and generate a new key for the new domain (production key).
After that, go back to the newly migrated website backend > Plugins > Add new > Commercial and register WPML with the new key (you might need to click "Unregister" first).
Sometimes, even after following the steps I mentioned above, you might still see that notice due to existing caching on the site or on the server/CDN (if used).
In order to clear the server cache, you would need to reach the hosting support.
In order to clear the site cache, please make sure that you clear/remove it from any existing caching plugin that you might have installed on the site.
I hope that you will find this information helpful!
