Counterterror Alert Act of 2017 This bill requires the Department of Justice (DOJ) to include in the national instant criminal background check system (i.e., the NICS database) information about an individual who is or has been under a federal terrorism investigation. A federal department or agency must submit to DOJ information about such individual. Additionally, if a licensed gun dealer requests a background check on a prospective gun buyer who is or has been under a federal terrorism investigation, then the NICS database must notify the appropriate division of the Federal Bureau of Investigation of the request and the pending firearm transfer.