Homeless Veterans' Reintegration Programs Reauthorization Act of 2017 This bill extends through FY2022 the Department of Labor's: (1) homeless veterans reintegration programs, and (2) homeless women veterans and homeless veterans with children reintegration grant program. Currently, the homeless veterans reintegration programs provide job training, counseling, and placement services to expedite the reintegration of homeless veterans into the labor force. The bill expands eligibility for the programs to include: (1) veterans participating in the Department of Housing and Urban Development-Department of Veterans Affairs (VA) Supportive Housing Program, (2) Native American veterans receiving assistance under the Native American Housing Assistance and Self Determination Act of 1996, (3) veterans who are transitioning from being incarcerated, and (4) veterans participating in the VA's Supportive Services for Veteran Families Program.