It is Louisiana state law that criminal damage to historic buildings or landmarks by defacing with graffiti is punishable with up to a $1,000 fine and community service, by which the offender can provide graffiti abatement.
The City is responsible for graffiti abatement on public property and property owners are responsible for their property. This is enforced through the Vieux Carre Commission. While property owners should not be punished for damage to their property from vandals, it is their legal responsibility to maintain their property.
Just remember the 4 Rs: Report, React, Rules, and Resources.