About 47,000 fines totalling Â£1.3m were issued during a trial to restrict traffic during the day.
The trial took place between August 2013 and April 2014.
Refunds can be obtained by calling City of York Council or by visiting the website.
Refunds were offered to drivers after a traffic adjudicator said the council had "no power" to issue fines because signage and CCTV were inadequate.
Last year, the council spent about Â£150,000 writing to 27,000 drivers who had not claimed a refund. The deadline has been extended twice.
The authority said it would publish the total cost of the Lendal Bridge "settlement" after 31 March when the application process ends.
It disputes the findings of the Traffic Penalty Tribunal "regarding the lawful ability to regulate traffic in this way" and said the trial was aimed at reducing congestion in the city centre, not making money.
Drivers fined for crossing York's Lendal Bridge while traffic restrictions were in place have just days to apply for their money back, officials have said.