Unlike most bandit groups, the player actually gets Bonus Experience at the end of the chapter for leaving them alive. This is because as Ranulf says attacking them would jeopardize the alliance between the Gallia and Crimea and perhaps the Vigilantes misguided belief that they are protecting their community.
The Vigilantes are composed of only three low level myrmidons who pose little threat to your units and are easily cut down for the most meager amount of exp. However as Zihark is next to them and the vigilantes attack your units on sight, leaving them alive and recruiting Zihark can be difficult so strategy is required.
One effective way to recruit Zihark and gain the Bonus experience is to deploy Mordecai and Lethe. Nearing the end of the map, Mordecai should use Smite on Lethe, allowing her to talk to Zihark without killing the vigilantes, after this is done your other units should step on the seize square thus ending the map before the vigilantes can act.
Another method is to have a transformed Laguz run to Zihark from behind and once again ending the map before the vigilantes can act.
Each living vigilante gives 75 exp on Easy or 50 Xp on Normal.