There are quite a number of things about GW scoring that do not make sense. For example, why count turns I make rather than turns the opponent makes? If my opponent never moves, not even a single time, does it really matter that I made 25 moves on my side to accomplish that?
But this note is specifically in regard to how Barrier is treated in GW scoring. From multiple instances and multiple sources, it is clear that damage done to your Barrier counts against you in GW scoring. This is so dumb, it has to be a bug. Zero damage was done. The GW calculations should be fixed to show that.