π Eid
Eidi has always been money, so there is nothing to justify here. The difficulty is distance: the tradition assumes you are in the same room, pressing a note into someone's hand after prayers.
Send a giftA bank transfer carries the money but loses everything around it, which for Eidi is most of the point. The giving is a moment, not a payment.
An illustrated card with your own words on it, opened on the day, keeps the shape of the tradition when you cannot be there. Useful for relatives abroad, for godchildren and nieces and nephews in another city, and for anyone whose family Eid is spread across several.
Other occasions