A fix that worked for me:

Rename or move your Documents\My Games\GalCiv3 folder

Start the game, letting it generate a new GalCiv3 folder.

Copy your first GalCiv3 folder back, choosing not to overwrite files.

What might work instead, is going into Properties on that folder, and making sure Read-only is unchecked

If that doesn't fix it - the Invasion screen still works, you just can't see the buttons. Just click on the bottom right of the box to start the invasion. Not ideal, but at least you won't have to close the game.