I'm a little confused. The rifle in the link is a Jeffery, not a Westley.

The Jeffery's of that model were offered with a third fastener as an option. It was a sliding bolt, round in cross section, that slid into the doll's head from the rear. It was not a screw grip. Some of these rifles have it and some don't.

Westley used several types, at least one of which was a screw-grip, but their usual "C-type" was not. It was also a sliding bolt.