The official website for The Settlers of Catan

Question about The Cards Arsonist - If my opponent prevailed against my Arsonist by using Heinrich the Sentinel or a Lookout Tower, and I only have buildings that are protected by a Fire Brigade - do I have to remove a building from my principality?

Answer

No. If he prevails, the Arsonist no longer has an effect, which is why it doesn't matter whether or not a Fire Brigade protects the buildings.