From what I've read elsewhere the requirement to mark goods imported to the USAwith country of origin has its roots in the McKinley Tariff Act of 1890. The Act was a misguided attempt to protect US industry from foreign competitors and products which were finding their way into the US domestic market. Ultimately the whole concept proved flawed and became widely unpopular, resulting in the act lasting little more than four years. However one feature which survived the ending of tariffs was the requirement that goods made outside of the USA had to be prominently marked with their country of origin prior to their entry into the United States. An example of this can be seen on the many Fairbairn Sykes commando knives surplused by the British
Government after WW2 and imported into the US. These are typically stamped "ENGLAND" on the crossguard. Similar examples can be seen with imported ceramics, e.g. marked "JAPAN".
Firearms would not have escaped this mandated compulsory origin marking and indeed there are discussions elsewhere about it in the context of English gun makers at the end of the 19th century.