Great question — answering as the UphillTech team:
No, US citizens and green card holders don't need to apply for ETA no matter the origin. See the Canadian Immigration Authority : Travellers who are exempt from the eTA requirement. U.S. citizens are exempt from the eTA requirement and must carry proper identification such as a valid U.S. passport. Lawful permanent residents of the United States who hold valid status in the U.S. are exempt from the eTA requirement. They must carry official proof of status (or an equivalent status document) and a valid passport from their country of nationality (or an equivalent travel document).
Full answer by oh whatever: https://travel.stackexchange.com/a/190725 (CC BY-SA 4.0).
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