Banking Restrictions Involving North Korea (BRINK) Act of 2017 This bill requires the President to: (1) submit to Congress a list of financial institutions that are providing financial or banking support to the government of North Korea; (2) impose specified financial and asset blocking sanctions on an institution that has knowingly engaged in such conduct, and (3) impose specified civil penalties upon a U.S. institution based upon whether it has taken steps to prevent a recurrence of such conduct. The President: (1) may suspend, renew, or terminate sanctions subject to prior congressional notification and review; and (2) may not take an action if Congress enacts a joint resolution of disapproval of such action. The President shall prohibit, with specified exceptions, transactions involving the manufacture, sale, purchase, transfer, import, or export of certain North Korean goods, services, or technology (covered property) by a U.S. person or such transactions that are conducted in the United States. The President may impose specified sanctions with respect to: (1) persons providing specialized financial messaging services to North Korean financial institutions or sanctioned persons, and (2) governments that fail to take specified actions against North Korean financial institutions or persons designated under a United Nations Security Council resolution. A state or local government may divest its assets from, or prohibit investment of its assets in, any person engaging in investment activities involving North Korean covered property valued at more than $10,000. The bill expresses the sense of Congress with respect to: (1) blocking of property of North Korean officials, (2) divestiture of certain employee benefit plan funds involving North Korean covered property, and (3) the Kaesong Industrial Complex and North Korean nuclear disarmament.