To understand this problem, you need to know that, when a diagram is linked to different locations (document and/or worksheets), the markers are stored individually for each location.
If you link a diagram to a document, then the document is storing the markers for the linked diagram along with other attributes like the individual horizontal and vertical dimensions of the linked diagram for example.
As far as we investigated the problem, there seems to be no solution for it currently. The reason for that is that the marker text in a linked diagram in a document is addressable only while the diagram is inplace active, which means it is displayed with a dashed border inside the document. Unfortunately, the Automation Object Model for FlexPro is missing a method to inplace-activate an object.
An alternative solution would be to address the markers through the CursorObject interface. When you change the marker text, then the marker closest to the active cursor in the active item (linked diagram) of the active CursorObject (Document) is changed. But the Object Model is also missing a method to address the active item in a CursorObject.
We will further investigate on this problem and extend the object model so that it will be possible to perforem the requested operation.