The only thing you could do is clip up as much hair as possible away from the edges where the tape is attaching the piece, then use an orange(citrus) based hand cleaner like permatex fast orange hand cleaner. spray some of that only on the tape and lace or rub in on (apply it with a brush) being careful not to get it on the hair.

I found this method really helps...then clean the rest of the remaining residue with pure alcohol...rinse it out and let it dry.
Taking your time is essential (thats why swapping one out with the other fresh piece is really a must when you are in a rush).