Try to deselect the Delta MIDI input (System settings / Harware / MIDI Port configuration / MIDI In Ports), ie. select none. Now play your keyboard (or whatever MIDI Input device) through your Finale. Does any of the MIDI Port lights at the bottom of GigaStudio window turn red? Then GigaStudio knows about Finale. If lights are green only, you should check that MIDI through function in Finale is turned on.
Thank you for those suggestions, Ondrej. Those MIDI lights are very useful. After a lot of playing around, I finally figured it out: GS3 recognizes Finale after you start using it as its "Editor". Works like a charm now.