The email you're referring to was sent by Upwork. Let us know if you have any questions about it or feel free to follow up directly on it. I also merged your post in the announcement thread where you can find more information about this.
At this time you cannot request to be invited. For the best chance of being invited in the future, we suggest freelancers achieve a solid reputation, keep a complete and up-to-date profile that is not set to private, and maintain an active Upwork account in good standing. You can find more information here.