Edwin's key has been stolen by a gang member of his in the hope that Edwin would cause a ruckus and be kicked out of his gang. Now Beckett wants the Vault Dweller to retrieve the key. Go to the indicated location, Treetops, and find the key in a trunk at the top level. Bring it back to Beckett to complete the quest.
Behind the scenes
"Out of key" is a phrase that means "out of harmony", or in other words, "not in agreement". In the context of the quest, it refers to two ideas: first, that Edwin's gang has been falling apart since the key to his cache was stolen, and second, that Beckett had a falling out with that gang when he stole Edwin's diary and is now trying to get back "in key" and make up for it.