Void Militia lowers the cost to defeat a Monster. In other words, if the player has accumulated 6 power on a turn and six cost Monster appears in the Center Row, the player would only need to spend 5 power to defeat the Monster. However, Void Militia's effect does not impact cards like Temple Guardian. Cards like Temple Guardian can only defeat Monsters with a printed cost that matches Temple Guardian's effect since the player is not paying any accumulated Power to defeat the Monster.
This same rule can also be applied to Aiyana's Messenger and Stone Circle Elder. Stone Circle Elder can only acquire cards with a printed cost for 5 or fewer Rune.