Not sure but I have tore up carpeting and the worst part is getting all of the many staples out of the floor. On the stairs especially! Oh man it was a never ending flood of stables.
What Id try (if I had this) is "goo gone" which I have had for a long time. It works wonders for getting stuff off. Even though its an old cleaner it is still sold in stores.
Final option: maybe one of those rug cleaner things you rent from walmart?