I just informally polled 3 native English-speaking teachers here. No one could come up for a term for the green verge. I think it is one of those things in the English language that needs a name but doesn't have an official one. I know there is a book full of those things, which themselves have a name, but I can't remember that either. (What do you call the metal plate around a skeleton-keyhole on old doors? A keyguard. What do you call the last dollop of ketchup or the like stuck in the bottle? I once knew. What do you call the little plastic cap on a shoe lace? I'd call it a telomere on a chromosome, but has it been called a lacecap?) My vote for a synonym to green verge would be the grassy margin. How about a truncated lawn?