A Google search wasn't encouraging. The top hits for the phrase "jewelry courier" weren't businesses offering their services; they were news reports about robberies.
True, most of those robberies were of loose diamonds, which are easier to fence and harder to trace than a necklace with a distinctive two-inch pendant piece like this.
But even if thieves had to break up the parrot and sell the gems individually—even if they destroyed the artistry of the thing—they would still have made a hefty profit.