My boyfriend uses the branded oil Trans Tape sells, but he only uses the tape occasionally, not frequently enough to have residual residue from multiple uses and I'd guess you'd have tried the solution the brand recommends first.
Another friend of mine says they pretty much bathe in oil to remove it.
I have been rubbing vaseline on the leftover adhesive to get it off. Sometimes I gotta scratch it then leave the lot of it to fall off over the day before showering.