The City Treasurer shall cancel outstanding refund checks after 6 years.  The amount represented by such checks shall be transferred from the refund account to the General Fund.  In order that persons having refunds due which are represented by outstanding refund checks may not be precluded from establishing their right to such refund in the future, any person entitled to a refund, for which refund a check has been issued and has not been presented for payment within 6 years, and which refund has been canceled under the provisions of this Section, may petition the Council at any time for the allowance of such refund.  The Council may after hearing upon such claim allow and pay the amount of such refund from the General Fund.  Such payment however shall be made only by ordinance.