What to do when UI element can't be selected by TC in a Keyword test?

I need to close a window of our Desktop Application, but the close box is inaccessible to TestComplete.  Object Spy can't see it, it only sees the entire window.

I found that I can directly call the CloseWindow method (or just Close) and that prompts the window to close, but our application always asks the user if they are sure they wish to close the window via a simple yes/no popup dialog.  If I invoke closing via the method directly, then these yes/no buttons are not able to be interacted with at all by TC, despite TC being able to see them fine.

If I manually click the close box, then let TC interact with the Yes/No buttons, they work fine.  So it seems to me that something about invoking the method directly, is freezing TC out of being able to see that the Yes/No popup has appeared.

I'd be happy to get either scenario working - getting TC to click the close button of the window, or invoking the method directly and getting TC to interact with the confirmation dialog.  Any suggestions on how to deal with such a situation?  I looked through the Freezing Diagnostics and tried to get it to tell me something, but it never produced any messages of any kind.