The Mona Lisa has been stolen dozens of times, most of them unreported. Every time the thief found that the painting was a copy. This usually meant an unpleasant death.
The pace of the robberies is picking up over time, so the very, very secret _Atelier de l'Etat_ has to produce copies faster than ever. The lack of the long-lost original could theoretically be a problem, but more than a century of continuous teaching and practice means it would now be redundant. _They_ are the Mona Lisa.
So they are the ones we want you to kidnap.