Picture a green card held out by someone in charge — an official at a desk, an insurer, an umpire on the pitch. The card itself does nothing; it is the green piece of paper that stands in for a decision already made about you. You may stay. You are covered. You have been warned once. In each case the colour is the label, and the card is the short way of saying the whole sentence.
From the word’s history
Wiktionary records that the US work permit is named from the historical greenish colour of the card, first used in 1946, and that the American Express charge card of the same name came from its green design made to resemble US dollar bills.
Wiktionary 記載：美國那張工作證件的名字來自卡片早年的綠色，最早在 1946 年使用；而同名的美國運通簽帳卡則是因為卡面設計成類似美元的綠色。也就是說，這些用法的共同點不是同一個來源，而是同一個做法——用顏色替一張卡命名。
Wiktionary, "green card"
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