Veterans Justice Outreach Improvement Act This bill updates the Department of Veterans Affairs (VA) Veterans Justice Outreach Program, which is a program through which the VA identifies justice-involved veterans and provides them with access to VA services. Justice-involved veterans are those with active, ongoing, or recent contact with some component of a local criminal justice system. Specifically, the bill requires the VA to conduct program outreach to justice-involved veterans, military and veterans service organizations, and relevant stakeholders in the criminal justice community (e.g., local law enforcement). The VA must increase the number of program specialists responsible for supporting justice-involved veterans in rural, remote, or underserved areas. Additionally, the VA must establish performance goals, measures, and implementation time lines for the program, specialists, and providing support for research regarding justice-involved veterans. Program specialists must receive training, at least annually, on (1) veteran eligibility for the program, and (2) best practices for identifying and conducting outreach to justice-involved veterans and relevant stakeholders in the criminal justice community.