On the accurate Barsky drawing from 1744 a Byzantine tower with the characteristic battlements is clearly visible, next to the entrance of Konstamonitou. On the photo of 1991 the tower is gone and replaced by a smaller one standing in the courtyard.
But not the whole tower is gone. The bottom part still belongs to the monastery walls. Outside and inside the yard.
My brother Wim took some pictures of the base of the tower. The widening bottom looks renovated.
In the courtyard the bottom of the tower is in scaffolding. I suspect they are repairing the joints as they did on the other side.