The rebate was brought in by the Conservative and Liberal Democrat cabinet after they ousted Labour from leadership of the council just days before the budget was due.
Labour had proposed a zero council tax increase, and the Lib Dems recommended a flat £30 rebate to all council tax payers.
However, the Conservatives introduced a 3% rebate, which ranges from £22 for a band A property to £66 for a band H home.
Councillor Green said a whole range of people would benefit from the rebate, including the poorest.
He said: “Clearly, this goes to pensioners on age-related benefit, and another group receiving it move in and out of benefit, and as they come out of benefit this will be applied to their council tax bills.
“I find it extraordinary the Labour Party are attacking me and my administration for helping the poorest people in Wirral.”
A spokesman for Wirral council said: “Households who are liable for council tax who receive 100% council tax benefit will receive a refund later in the year providing they do not have any monies outstanding.
“No refunds have yet been made and we will look to see how this is best undertaken. We will ensure that any outstanding debts are met before any payments are made.”