I guess as the private plate has to be relevant to the leasee and not the nominated driver which unfortunately you are, even if your the only driver, and thus they needed to speak to the leasee not the nominated driver to remove the plate.
Plus as it’s being taken off and put on retention and not transfered directly to the new car it needs to be put in a persons name and as far as Mb are concerned that’s the leasee and thus probally is the reason/need to speak to your wife to confirm that is in fact the case, i’d be more concerned if they didn’t.
Also guessing when it was put on it was/had to be in your wifes name.
I don’t have that problem as i am the leasee and the only driver and the plate is relevent to me.