Can I submit a background check that I can have completed outside of Rover?

No, you have to use the company that Rover has contracted with to perform these checks. You can call Rover Customer Support at [Edit: Rover’s contact options have changed. Visit the Rover Help Center at https://support.rover.com/ to find the phone number, help articles, or chat with the team] to discuss, but everyone admitted to its platform does have to provide the info to that company.