GB Studio doesn't use a green palette actually. The green tones are just for building.
When started in the internal emulator or web application it will act like a Game Boy Color and automatically pic these weird green, blue and red palette, if I remember correctly.
It let's you choose different palettes by using the arrow keys and A and B button.
But you can force a palette nonetheless, like some original games also did. I figured that out a while ago.
*I'm currently at work / not at home, so you have to wait a bit for a tutorial, but it's totally possible.