I've seen the route spelled "Mithral" (e.g. here, in SuperTopo, in Croft, and in Porcella & Burns) as well as "Mithril" (e.g. in Moynier & Fiddler).
Moynier & Fiddler give convincing evidence that "Mithril" is correct. They claim that it is named after the fictitious metal "mithril" from Tolkien's "Lord of the Rings" series; whether this is what Bartlett and Roberts named it after is maybe unclear, but if it is true, then it is definitely "mithril" (just do a Wikipedia search on "mithril").