|The following is based on Fallout Tactics and some details might contradict canon.|
The ghouls there requested help due to Super Mutant attacks. This led the Brotherhood to believe that the mutants were after the ICBM the ghouls worshiped.
The Warrior's team was sent in to defend the ghouls in exchange for the ICBM. They fended off the attackers and killed all three mutant commanders there. The initial Super Mutant offensive was crushed.
Later on, Smear and Shadow Squads fought off the bulk of the forces sent after the first offensive was destroyed; after which they stood watch until Gravestone was confirmed to be safe from the mutant threat.
The Bishop proved true to his word and provided the missile to the Brotherhood. Captured Beastlords and raiders hauled the radioactive nuke to an underground, lead shielded bunker under armed supervision of course. With both Rad-X and Rad-Away supplies used only for high priority missions, the prisoners were exposed and presumably died of radiation poisoning.
The mutants' experienced horrific losses and the battle was their last recorded offensive attack before their defeat in the Invasion of Osceolla.
The Battle of Kansas City appears only in Fallout Tactics.