The National Historic Landmarks program is administered by the National Park Service. http://www.nps.gov/nhl/ As such, the same rules apply there as in the rest of the National Parks.
Thank you for volunteering to contact the Superintendent there about correcting the sign. (HINT - if you don't do it, who will? Why wait for someone else to step up? IF there is resistance you can call on VCDL for assistance, but I seriously doubt the Superintendent would give much resistance to a suggestion that the judicious use of duct tape or paint might rectify the situation.)