I recently had excellent success removing old tape residue from my carpet using the method recommended at the following website. (Actually I had to call them to get directions for tape, but I do see "grease" is on their list on the website, and tape was not.)

Good luck.

If you are uncertain about the cleaning instructions on the website, you can call them. A very nice woman helped me, and I am so happy to have gotten the tape marks out after looking at them for nearly a year. Our painter used duct tape to tape down paper to "protect" the carpet. It left a sticky residue which collected dirt, and even the professional carpet cleaners could not get it out.

Hope you have success too. If your instructions include putting paper towels down and putting a weight on them as the last step, the lady told me this is very important, don't skip it.

Good luck.

Susan