Tiahrt Restrictions Repeal Act - Amends the Consolidated and Further Continuing Appropriations Act, 2012, to repeal prohibitions on using appropriated funds: (1) to disclose contents of the Firearms Trace System database maintained by the National Trace Center of the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) or any information required to be kept by firearms dealers except as specified in such Act; (2) to promulgate or implement any rule requiring a physical inventory of any firearms business; or (3) for any background check system that does not require the destruction of identifying information submitted for a transferee within 24 hours after the system advises a federal firearms licensee that the transferee's receipt of a firearm is not prohibited.