I would just give it to me because I don't mind if it is dirty.
I used easy off on stainless material before (not on aluminum) and it works fairly well. In a well ventilated area and gloves. Watch your eyes because its sodium hydrxide.
Heat is the key with the other style of cleaners. I used simple green and scalding hot water before and its more of the heat than the simple green that works. On my Popperette umbrella (inner flap piece) I used a torch and pipe cleaners once until the solder melted, but I did remove the oil.
I would bet you that the oil used was not coconut oil. I never ever had a problem with coconut oil. It sounds more like corn or vegetable oil your dealing with. That stuff is a pain in the ... to remove.
When I had my Popperette's paint saturated in baked on veg oil, I ended up using Goo Gone to remove the oil from the paint. The paint was saved, polished, waxed, and then I only used coconut oil after that. No problems since then.