Given that TW has not only reneged on both recommending and presenting the offer he agreed with BA to Unite's CC members but now has also come out with a renewed set of conditions and announced a fresh strike ballot, I am very surprised that BA has not withdraw its current offer as it did last time.
BA both offered and even made (as a goodwill gesture) substantial concessions on ST and to its established disciplinary procedure for IA related cases in return for nothing whatsoever from Unite. It makes no sense that BA should leave this offer on the table now that further damage to both future bookings and its brand image will have been incurred by TW's announcement and particularly as Unite has clearly shown its distain towards it.
As far as ST is concerned, tactically, I think it would be better not to withdraw staff travel again. Someone who had lost ST, only to get it back in part and lose it again may think they have nothing to lose by striking again. The risk of losing staff travel again may make some think again about striking this time, having learned the hard way that it would not be reinstated "in five minutes!".