Wiped down all surfaces with slightly moistend towels, pictured with hands after washing a second time. Took Lysol wipes to it after that because I care a lot more about the clothes I’m putting on it than if I damage the finish and got a bit more of the black dye out.
https://www.amazon.com/ClosetMaid-421-Cubeicals-Organizer-9-Cube/dp/B000ETOG6G