Restringing Monet Necklace

I am trying to restring a Monet necklace which has a pendant.

However, the pendant has an insert which is glued in the same grove
as the holds for stringing the cord. I do I remove the glued insert
which is plastic or some sort of Lucite without damage? It is a
favorite necklace of a customer. I have attached a photo for

Thank you for any assistance you can provide.