Veterans Benefits Improvement Act of 2023 This bill addresses certain requirements related to Department of Veterans Affairs (VA) medical disability examinations for purposes of benefit claims and other administrative matters related to the benefit claims processes and personnel. First, the bill updates procedures related to the publishing of VA disability benefit questionnaire forms. Specifically, the VA does not have to publish certain forms if it determines the form could not reasonably be completed to a clinically acceptable standard by someone who is not an employee or contractor of the VA. The bill also requires the VA to report on its efforts to provide reimbursement for a veteran's travel to a facility, regardless of whether the facility is inside or outside of the United States, when such travel is incident to a medical disability examination for purposes of VA benefits. The VA must also include certain elements in contracts it enters with non-VA providers to provide medical disability examinations. Specifically, the contracts must require that every communication from the provider to the applicant regarding the scheduling of a medical disability examination must be transmitted to any person or organization that is legally designated by the applicant and is recognized for the preparation, presentation, and prosecution of claims. Additionally, the VA must partner with veterans service organizations and other stakeholders (as determined by the VA) to implement an outreach program for veterans regarding (1) contact information for non-VA providers that are providing medical disability examinations, and (2) the requirement for veterans to provide personally identifiable information when contacted by such providers to verify their identity. The VA must report on improving its support of governmental veterans service officers. The VA must establish a Board of Veterans' Appeals internship program for individuals enrolled in the first or second year of law school. The VA must also implement a program to furnish student loan repayment benefits or reimbursements for courses, bar exams, or bar membership dues to certain attorneys who agree to work for the VA for at least 3 years. The bill increases the maximum possible number of judges presiding over the U.S. Court of Appeals for Veterans Claims to nine judges. Finally, the VA must report on improving access to telehearings for Board of Veterans' Appeals hearings.