Help Needed with Saving PDF Using Keyword Test: Window Overlap and Index Issue

It is odd to have two print dialog boxes overlapping. When printing from an application logically you are dealing with a single dialogue. I question it if it is part of your application normal behavior. I would focus on solving that rather than solving the overlapping dialogues.

When you use spy to identify and map such object, in NameMapping you should be able to highlight https://support.smartbear.com/testcomplete/docs/testing-with/object-identification/name-mapping/how-to/locate/highlight-in-app.html such object signaling that detection is valid. Also in NameMapping you can Modifying the identification criteria https://support.smartbear.com/testcomplete/docs/testing-with/object-identification/name-mapping/editor/index.html to something unique in cases such as yours.

Your application should only display one "Save Print Output As" dialog. Though it might not be a bug, it's not a good Windows UI application to show more than one dialog like that.