G'day Stashu,
Yes, all the oil residue needs to be cleaned off, I just use the stuff I clean my plane with, after flying, both the underside of the trim & the base covering.
Use a sealing iron, or household iron, if you don't have anything else, start with the iron cool & slowly get it hotter until the trim sticks, then when it's back down, paint the edges of the trim & any other covering edges, with clear nail polish, it is fuel proof & nearly invisible, & is very cheap & one bottle goes a very long way, & only takes seconds to dry.