Purity of War is a mask you get by finishing "The Undying Flame", from Mythic Tale. It is a story reward, so playing the tale is the only way to add it.
Play "The Undying Flame" to the end and the mask comes with the rewards.
Izanami's Grief
Izanami's Grief is a Sword Kit for Jin's katana and tanto. It is a reward for finishing the Mythic Tale "The Undying Flame", and like every kit it changes looks only.