Does the aforementioned wife deserve a dowry after it became apparent that she was not a virgin and the husband divorced her?

The hymen may be lost due to permissible causes and without the woman's knowledge, so do not rush to accuse and divorce. If you find something in her that displeases you, you might find something else in her that pleases you even more, and "No believing man should hate a believing woman; if he dislikes one of her characteristics, he will be pleased with another." Strive to reform her and do what strengthens faith and instills the fear of God. If you insist on divorce, your wife is entitled to the full mahr (dowry) upon consummation (intercourse), and a publicized wedding is not a condition.