The story
Origin unknown. Since formal letters are usually written in black or blue ink, perhaps there is a suggestion that only eccentric people use green ink.
First known use, by meaning
- from 20th c. Collectively, those people who write letters to newspaper editors, politicians, etc., expressing eccentric views; the letters are often stereotyped as being lengthy, handwritten in green ink, and characterized by the frequent use of capital letters and underlining.
Etymology from Wiktionary, CC BY-SA 4.0.