Putting Our Veterans Back to Work Act of 2017 This bill amends the: (1) VOW to Hire Heroes Act of 2011 to extend through 2020 the veterans retraining assistance program, and (2) Wounded Warrior Act to extend through 2020 the authority of the Department of Veterans Affairs (VA) to provide the same rehabilitation and vocational benefits to members of the Armed Forces with severe injuries or illnesses as are provided to veterans. The bill extends through: (1) March 31, 2020, additional VA rehabilitation programs for certain disabled veterans who have completed a VA rehabilitation program and have exhausted their rights to state unemployment benefits; and (2) FY2021 the collaborative veterans' training, mentoring, and placement program. The VA shall develop a single, unified federal web-based employment portal for veterans to access information on federal programs and activities concerning veterans employment, unemployment, and training. The bill directs the: (1) Department of Homeland Security to award grants to hire veterans as firefighters, and (2) Department of Justice to award grants to hire veterans as law enforcement officers. The head of each executive and defense agency shall consider favorably, as an evaluation factor in federal solicitations for civilian or defense contracts and task or delivery orders valued at or above $25 million, the employment by a prospective contractor of veterans constituting at least 5% of the contractor's workforce.