Using ice will harden those stretchy putty and eventually make it easy for you to break it down to remove it.
With a loose knife, you can break or scratch the silly putty. By this, the putty will loosen out of carpet fibers and be removed easily.
Nail Polish contains acetone and ethyl acetate, which are strong solvents that draw nail polish from any surface.
Add detergent or liquid dishwasher into water and soak a cotton ball in the prepared mixture and apply it on a hidden part of the carpet.
Vinegar is made of about 5% acetic acid, which helps it to break the structure of any dirt or oil. The only problem with this idea is that this acid agent can harm a few fabrics.