Cologne responded, according to German newspaper Express, by sending an invoice for $184 to Hitz. The sum is reportedly to cover new turf and two hours of skilled labour.
Augsburg added on the Facebook page that the club doubted the repairs would take two hours and that they would send Cologne a lawnmower - "with a wink".
Anthony Modeste, who has not scored since 4 October, slipped badly and saw his penalty saved by Hitz, whose disruptive gardening efforts paid off and the away side won the game 1-0.
Hitz wrote on Augsburg's Facebook page: "If the bill was sent with a wink, I would like to pay on receipt, even if I think that our groundsman could mend the penalty spot faster."
Cologne have said they will donate Hitz's payment to a children's hospital.