Actually "card" is an appropriate translation, as long as you're talking about the kind of card you might receive in the mail, like a thank you card, or a birthday card.
I wholeheartedly agree. As someone who grew up speaking spanish, I would undoubtedly occasionaly refer to a "card" in place of "letter" when using that word
The only time "carta" means "card" on duolingo is when it is "shows his/her/the/etc card(s)". My guess is if it does not sound like a typical card playing move or you are not playing cards then it going to be understood as "letter".
Duo's answer was 'They are going to receive my lcard'. What is an 'lcard'?