There seems to be something "special" about FB Award Bookings.

I was in the Crown Lounge in AMS last week, travelling on an FB Award, and using my AZ Freccia Alata card for lounge access. Unprompted, the desk agent proceeded to try to overwrite my FB number in the booking. She couldn't. She appealed to her colleague. Together, they spent several minutes huddled together, trying to figure out how to overwrite my FB Ivory number (while the queue for access lengthened behind me) until eventually she asked: "Is this an award booking"? I replied yes, and they instantly ceased all attempts to update the number, as if this appeared to satisfy them that their labour was in vain. [Whether this means that FB/KL was now on the hook for paying for my visit to the lounge, rather than AZ which would have been the case had they managed to successfully update the FFP number, I do not know].

Of course, no miles can be earned anywhere on an Award Ticket, so it might be a "feature" that FB bookings cannot be disociated from the FB number used to make them (Bear in mind that, when you travel on an FB award made by someone else, that other person's number remains associated with the booking, and is printed on all boarding passes, in contravention of all "normal" rules of the programme).

Don't attempt to change it - it won't change. Just bring the Alitalia card with you. If a lounge/checkin agent takes it upon themselves to try to change the number, let them - but I don't expect that they will succeed.