You did not mention, for which version.
I have PhotoDirector 9 and 10:
Not in the way, that you click on a color (green) and it disappears. But in the layers tab you can select with a "smart brush", that respects borders of different colors. So you can select your greenscreen and then remove it with the erasure tool.
You can do similar in the edit tab with "Background removal" and use of the "intelligent brush" (Everything today is "intelligent". What a crap.)
Hatti
Win 10 64, i7-4790k, 32GB Ram, 256 GB SSD, SATA 2TB, SATA 4TB, NVidia GTX1080 8GB, LG 34" 4K Wide, AOC 24" 1080