Millenco Lockmaster Mantis 3 lock - extra part after rebuilding
Per @Ecnerwal's comment, it appears to sit astride the spring just above the keyhole, with the ends of the horseshoe slotting into holes in both faceplates when they're re-assembled...:

I'm having trouble getting the other faceplate on without knocking all the parts around, but that's a different problem althogether...