cartridge extractor - a mechanism in a firearm that pulls an empty shell case out of the chamber and passes it to the ejector

cartridge remover, extractor
http://www.thefreedictionary.com/cartridge extractor

Ejectors – Fittings inset into the breech end of a pair of barrels of a break-open gun, operated by a spring mechanism built into the forend, that kick out fired shells, while only raising unfired shells enough to be removed by hand. Recognizable at a glance on the breech end of a double gun because the fitting is split in two---one ejector for each barrel.

Extractors - A fitting inset into the breech end of a pair of barrels of a break-open gun. When the gun is opened the extractor lifts the cartridges so they may be removed by hand. Recognizable at a glance on the breech end of a double gun because the fitting is solid---one extractor taking care of both barrels together. Sometimes called Lifters.
http://www.hallowellco.com/ejectors_and_extractors.htm

An extractor is a part in a firearm that serves to remove brass cases of fired ammunition after the ammunition has been fired. When the gun's action cycles, the extractor lifts or removes the spent brass casing from the firing chamber.

Extractors or cartridge pullers can be tools to pull out bullet shells, used as a small gudget with three claws that come on a ring or mounted on some rod ...
en.wikipedia.org/wiki/Extractor_(firearms)