GooGone works for most tape residue. Some require more elbow grease than others.
I'd try to limit the amount of cleanup by slicing the tape with a mat knife and adjustable square or a sharp marking gauge about 3/4" in from the jamb face and rabbeting the edge of the extension jambs to fit over the remaining tape. I'd start with a heat gun and putty knife to lift the tape and follow up with solvent and a sharp scraper. Alcohol, acetone and mineral spirits are usually on my shelf. As said, try for advice from the manufacturer. Maybe you can get the guy who installed the tape to remove it.
I've always used 3M Adhesive Remover; however here on the Left Coast - it is now illegal!
WD40 seems to work as good as any other adhesive remover. After all it is primarily a solvent. But on wood? Key is it to let it soak for a few minutes.
NOW you tell me...