Bob,
I have seen this many times on synthetic carpets - friction-heat causing minor surface melting.
Success rates vary between total removal, removal of deposited material but pile damage still evident to minor improvement only.
I have used several methods in the past but in the past 6 months have dealt with the problem twice, using Eco spotter and a bone scraper. Prior to the availability of this product the best over-all success has been with isopranamol and a scraper. In both cases the alcohol serves as a penetrating wetting agent which assists in breaking the bond between the two plastics.
Work slowly and carefully and promise nothing.