Well the building is Grade 2 listed so the eagle may be part of that protected frontage that cant be changed.
However the US may argue the Eagle is not part of the design of the building so can be removed.
I have searched the web and can find no article saying what will happen to the eagle.
The building was bought by Qateri Holdings a number of years ago for 500 million dollars (not verified) and they plan to change the building in to a luxury hotel.