Are you comfortable allowing us to perform a criminal background check?

Undergoing a background check of any kind is standard for the airline industry. Safety and security are always a priority. United Airlines background check typically takes "about a week, maybe longer depending on the circumstances." So be prepared to agree to such requests. If you have concerns about anything that might turn up, don't try to hide it or hope it won't be noticed. That lacks integrity. Instead, be honest about it and take advantage of the opportunity to provide context to those items. This could give you an upper hand in controlling your narrative.