Set background color as transparency color in both your layers and your frames
I don't use GG sadly, but I did find this video in case you haven't tried that yet - it mentions PNG files but hopefully it works for animations as well.
Also, that's a really cute Clefairy
(Anyone know how to make a gif transparent, btw? I can't seem to do that in GraphicsGale - not entirely sure whether that's a software limitation or I'm just dumb.)
I was wondering why this seemed familiar! I forgot about that Pokemon Stadium game, awesome throwback and use of color!