The GB tax to which you are referring is a ticket tax, that is it must be collected at the time of ticketing. Even if it is not collected by the airline that issued your ticket, presumably your emplying airline, bBA will bill them for it.

Like most taxes, the rules for collection of the GB were written to apply to commercial passengers. And the GB rule says it does not apply if you are transitting for less than X hours. Because staff travel on standby tickets there is no guarantee to the ticketing airline or the transporting airline that you will make a connection with X hours or, for that matter, that you actually intend to.

Unlike employees, commercial passengers generally buy a fare that differs based, in part, on whether they intend to stop-over (say more than 24 hours) or to connect. A connection usually costs less than a stopover and the taxes applicable differ. The commercial passenger is then bound to the ticketed itinerary. If s/he choses to change the itinerary from a connection to a stopover, then the itinerary has to re-priced and re-ticketed, likely, at a higher fare. The ticketing airline then also collects the correct and applicable taxes. This is not the case for employees.

In short, I don't expect your airline to waive this tax because BA (or which ever is the transporting airline) will bill them for it anyway. Your airline would then be footing the tax bill for you to travel.