I got another wonderful answer last week (for different ticket HEL-MAN-HKG) and the system wanted to charge 50e for an exit row HEL-MAN (again it should be free with a BAEC gold card on the reservation).
CS said that the 50e was a discount and the full price of an exit row for HEL-MAN is 150e and I get it at a discount because of my emerald card!!
In that case going to CX manage my booking, removing my BA number and then adding it back cleared the problem when I went back to the finnair manage booking page and the exit row became free of charge.