What did the king take back from Haman and give to Mordecai?

Answer: His signet ring

The king had given Haman his signet ring; after Haman's death he gave it to Mordecai, and Esther set Mordecai over Haman's estate.

“So the king removed the signet ring from his finger and gave it to Haman son of Hammedatha, the Agagite, the enemy of the Jews. The king removed the signet ring he had recovered from Haman and presented it to Mordecai. And Esther appointed Mordecai over the estate of Haman.”— Esther 3:10, 8:2 (BSB)