Heck, it’s green, and no one’s mentioned it yet. And it’s been around longer than Midori.
Hey man, hope you’re doing well. I just watched the movie and had the exact same question pop into my head when I saw that cocktail — it’s kind of a hobby of mine. There’s really no direct info about it online (I even considered emailing Samuel L. Jackson for a second!), but then I figured there might be a script floating around somewhere — and I found it!
“At the bar, we see Stacks Edwards and his girlfriend dropping shot glasses of green creme de menthe into large glasses of chilled Dom Perignon”
So, there’s your answer. Looking back, it’s actually kind of obvious — creme de menthe shows up symbolically in a few scenes throughout the movie, so this one’s no exception.
Hope that finally brings you some peace of mind after all these years 
You can check it up by searching for a script of Good fellas movie, it’s in open access.
Sorry if unrelated to the OP, but we ended up with a full bottle of Midori after a college party. More of an apertif IMHO, but the following week it was the only booze we had in the house and split the bottle between two of us, drinking it straight. Nasty stuff. While it’s green, you’ll be pooping blue smurfs the next day.
I kinda love the “Death In The Afternoon” foreshadowing. It sure smells like a Scorcese move to me.
Side-note kinda. I worked on a low-budget movie as a Steadicam Operator on the Jersey Shore. It was off-season and so the immense indoor arcade was empty. ( No clue which town…not way down the shore, more mid-coast ). Frank Vincent, who played Billy Batts, did a cameo. He and his wife were lifelong friends with the director’s parents. I walked up with my rig on and he gave me a knowing smile. A bit of chit-chat. Lovely fellow, incredibly polite and listened to the next-generation Director ( who he’d known since the guy was a small kid ) respectfully and did as directed. He was a pro and I was sorry when he passed away.
Same logic as in the workplace. If you create trouble for the boss, you get fired. If you don’t cause issues for the boss, they keep you around.
And a grasshopper was a very popular drink at the time.