I'm not sure of oderless mineral spirits are the same as regular mineral spirits (nonodorless?)-- anyway, oderless mineral spirits can, according to the packaging, be used to revitalize your dry tuff cloth. I used it on mine, and it worked pretty ok, but you would probably be better off getting some tuff glide--mineral spirits is only the carrier/solvent, not the active ingredient, so every time you use it, you dilute the active ingredients a bit.
--Josh