The overdrafts were valid until January 15, 2013, and limited to the value of the total amount of payments which had been delayed.
"I encourage affected school staff to get in touch with their bank so they know they're covered and can have some peace of mind over the holidays," Mr Hope said.
One who will not be taking up the offer is Purakaunui School secretary Jacque Ruston.
Financial relief arrived for her this week when she was finally paid under the Novopay system.
The single mother of two went unpaid for nearly four months and relied on bank loans and interest-free loans from friends to pay her mortgage and other living expenses.
However, the banks' offers may take the pressure off other frustrated school staff who continue to have problems.
Andrew Pearce, a relief teacher working in Dunedin schools, said he has not been paid for work he did at George Street Normal School on October 25, October 30 and November 1.
Instead, he was paid for a day's work on November 13 - a day he did not work there.
"Well, here we are at Pay 18 now, and I still have not been paid for these days. I guess it's two out of the three that I am waiting for because November 13 must have been one of them.
"So once again, I am going to be waiting well over a month to get paid for days that should have been, and were apparently, dealt with some time ago.
"I don't think the problems are going away anytime soon."
Ministry of Education group manager Rebecca Elvy said the latest pay round for school staff went smoothly, with more than 92,000 staff paid this week, and believed it was encouraging to see the steady progress being made with Novopay.
The ministry and Talent2 were working to ensure all staff were paid as expected for the Christmas period.
"It's great that nearly 90 per cent of schools have now completed the end-of-year pay process and we are working to support those who have yet to supply their information through both direct calls and visits from expert advisers," Ms Elvy said.
She assured anyone whose pay was incorrect leading up to Christmas would be able to contact the ministry to make sure they received their correct pay "promptly".