"recouper" means "to cut again". You have here a _touch-up_ operation by cutting, a "cut-up". Nice and creative translation, I would say.
While ‘recouper’ (verb) can be translated as simply ‘to re-cut’, it
is perhaps instructive to look at the root verb ‘couper’ for the
underlying meaning-set (spectrum of meanings).
The root verb ‘couper’ has several meanings that include ‘to cut
down’, ‘cut off’, ‘chop’, ‘slice’, ‘spoil’, ‘dilute’ (e.g. wine), and
even ‘slice’.
Also, while this looks to be a verbal-use one would have to examine
the original use in French to know for sure. It could also be a
clever or idiomatic use of a noun/verb mix (e.g. ‘A re-cut’).
The root noun would be: une coupe - a cutting, cut-out, cut, haircut,
cup (e.g. La Coupe du Monde ‘The World Cup’), bowl, glass, section
While I don’t know what the term is in French idiomatic terms of
jewelry, I would bet it is some one or more of these.
For me the word ‘recoupe’ does leave one with the idea of a
‘touch-up’ through the method of cutting, since one would not need to
‘re-cut’ without an initial ‘cut’.
Just my $.02.
Cheers!
Christopher