Easy. If a particular brand/model/configuration/caliber/serial number range was never manufactured here in the US, then it must have been imported. If so, it must have the importer's information.
Even if it were manufactured here, exported, and reimported, there is a record of that somewhere. Not likely to cause a problem as most LE/ATF won't be looking for that kind of thing unless the gun is used in a crime.
What if it gets stolen, used in a crime, and recovered. How will you explain the careful removal of the importer's mark. No thief would be that careful removing markings.