When someone has one of the "costs 6 gold to build but worth 8 at the end" purple districts in play, such as the Dragon Gate, does it cost the warlord 5 gold to destroy it or 7 gold?

Thanks

5 Gold to destroy University / Dragons' Gate

The Warlords ability costs 1 less than the build cost. As the build cost is 6, then the destruction cost is 5.

The value of 8 is only used for points value at the end of the game.