While we do not know Undauntra's House, we might speculate that given her awareness of the defensibility of a structure, it is one of the more martial ones; perhaps Dzur. Her name sounds like it is meant to evoke the English word "undaunted" (undismayed, "not forced to abandon purpose or effort"), again evocative of heroic Dzur or perhaps persistent Tsalmoth ("Tsalmoth maintains though none knows how") or ambitious Tiassa.