Gun Records Restoration and Preservation Act This bill amends several appropriations laws to remove limitations on the authority of the Bureau of Alcohol, Tobacco, Firearms and Explosives to conduct activities related to the administration of federal firearms laws. Specifically, the bill removes provisions that limit the use of firearms tracing data, limit the disclosure of data under the Freedom of Information Act, prohibit imposing a requirement that gun dealers conduct a physical inventory, prohibit consolidating or centralizing records maintained by federal firearm licensees (e.g., gun dealers), and require national instant criminal background check records to be destroyed within 24 hours.