What is the origin of the custom to send a greeting card?
The oldest source mentioning the Shana Tova card is in the book of the Maharil, Ya'akov HaLevi Mullin, one of the greatest poskim who lived in Germany from 1365 to 1427. He lived in Maagneza, Mainz, from which he issued an order to all Ashkenaz.

The Maharil collected and established religious customs in Israel and was considered an expert on Jewish customs in Germany. He was famous in his day as one of the greatest scholars of his generation, proficient in all the religion's customs.
So wrote the Maharil in his book, "The customs of the Ashkenazi communities": "When Elul enters, when a person writes a letter of peace to his friend, he should hint at its beginning that he seeks to return good for the year that will come. The word "return" probably means to refer. "