Neutralizing sulfur-like smells in car
I guess that it actually was a silver cleaner, not one for gold or precious stones.

The latter mostly contain nonionic surfactants, which are made by the reaction of water-insoluble long chain alkanols (C12 - C15, from natural fatty acids) with oxirane. These washing agents dissolve well in water and help to remove grease and fingerprints from the jewelery. Their action isn't much different from that of a dishwasher for manual cleaning.

These cleaners don't smell the way you described and the car retailer probably used similar cleaners for the car.

Silver cleaners are a different league. The do contain the same surfactants (washing agents), but in order to actually remove the tarnish (silver sulfide) from the silverware, they do also contain a bit of acid (typically sulfuric acid) and thiourea, which probably is responsible for the smell.

Repeated shampoeing probably is the best method to get rid of the thiourea without ruining the carpet.