Senior Financial Empowerment Act of 2017 This bill requires the Federal Trade Commission (FTC) to disseminate to senior citizens and their families and caregivers information regarding mail, telemarketing, and Internet fraud that targets senior citizens. The information must: (1) teach safe and smart financial practices, (2) provide instructions on how to refer a fraud complaint to law enforcement, and (3) include a toll-free telephone number that connects to a live individual who answers calls from seniors seeking advice about scams or how to report instances of fraud. The Department of Justice may award grants for the prevention of senior citizen fraud to state attorneys general, state or local law enforcement, senior centers, or nonprofit organizations that provide assistance to seniors. Priority shall be given to entities with public-private partnerships with computer or software companies that develop Internet scam prevention tools. The FTC must provide education regarding legal obligations, and concerning industry best practices addressing financial exploitation and neglect of seniors, to: (1) depository institutions, credit offices, remittance transfer providers, and general-use prepaid card distributors; and (2) financial institution employees who may be able to identify elder financial abuse. State agencies may not receive federal funds under this bill without ensuring that such financial entities in their states receive training on recognizing and reporting financial exploitation and neglect of seniors. The National Institutes of Health must research the increased vulnerability of seniors to scams and fraud due to age-related health and neurological conditions. The bill expresses the sense of Congress that a week in March of each year should be designated as National Senior Fraud Awareness Week.