The Charlotte Observer reported Saturday that investigators don't know exactly when the door was vandalized. The incident remains under investigation.
The lighthouse was completed in 1870 and is said to be the tallest brick lighthouse in the U.S.
"Graffiti is vandalism and is often extremely difficult to remove," the National Park Service said in a statement. "Repair of vandalized sites, if possible, is costly and time-consuming -- and may not restore the site to its former condition."
The National Park Service asks that anyone with information call the tip line of the National Park Service's Investigative Services Branch at (888) 653-0009.
Tips also can be submitted online here or here.