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.

The 24-year-old Mali international missed most of last season with a cruciate ligament injury, but has played 19 matches this term.
Head coach Paul Lambert told the club website: "He has been great since I have been here having come back from a long-term injury.
"And he is still only a young guy. He has his whole career in front of him."
Dicko scored 15 goals in 40 appearances for Wolves in the 2014-15 season, but his injury lay-off meant he played just six matches last season.
His only two goals so far this term came in the EFL Trophy victory over Crewe in October.
Lambert added: "Players like Nouha are really difficult to find, with such genuine speed.
"He is a major threat to opposition defenders with his pace and now I think he just needs to get a goal under his belt."
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.
[NEXT_CONCEPT]
Striker Nouha Dicko has signed a new deal which will keep him at Championship club Wolves until 2020.