Better Foreign Policy Through Better Pet Policy Act This bill authorizes the federal government to pay a foreign air carrier to transport a pet accompanying a federal employee's international travel in certain situations. Under current law, the official air transportation of federal employees, their dependents, and their property must be purchased from a U.S. flag air carrier (or authorized affiliate), subject to limited exceptions. Under this bill, if no U.S. flag air carrier is willing or able to a transport a pet accompanying a federal employee's international travel, the federal government may pay a foreign air carrier to provide for the transportation of the traveling employee, their accompanying dependents and property, and up to three pets. The bill caps such payments at the amount that would have been paid to a U.S. flag air carrier for the same travel and specifies that the federal employee must pay any difference. Dogs and cats are covered under this bill, with other animals subject to the approval of the Department of Transportation.