The actual expression is "για τα μάτιια του κόσμου" (gia ta matia tou kosmou) = for the eyes of the world. We say it when we have to do something (even though we don't want to) just so the others don't say anything about us, criticise us etc. Usually is for something that most of the people would think is the right thing to do although we don't feel like doing it.
In other words she should have apologised even if she didn't mean it because that would have been the right thing to do.