There are two places to delete a card: the card detail screen, and Translation History. They behave differently, so this article covers both.
Deleting from the card detail screen
Open a card and tap the three-dot menu in the top-right corner. A dropdown appears with Edit and Delete. Tap Delete.
A confirmation appears: "Delete card? This card will no longer be scheduled for review." Tap Delete to confirm, or Cancel to back out.
Once confirmed, the card is removed from its deck and from the review queue immediately. You're taken back to the previous screen, and a confirmation toast appears.
This deletion is permanent. The card does not appear in Translation History afterward, and there is no way to bring it back.
Deleting from Translation History
The 
history icon in the Translator screen's bottom toolbar opens Translation History. Each row has its own delete action alongside Edit.
Tap it, then confirm "Delete Flashcard? Are you sure you want to delete this flashcard?"
Unlike deleting from the card detail screen, a card deleted this way doesn't disappear from the list. It stays in place with a red Deleted label in place of its Edit and Delete actions.
Restoring a deleted card
Tap the Deleted label on any row showing it. The card is restored immediately: it reappears in its deck and rejoins the review queue right where it left off, and a "Translation restored" confirmation appears.
Effect on statistics
Deleting a card, either way, does not erase your review history for it. Past reviews of that card still count toward your overall statistics even after the card itself is gone.