The entitlement is limited to former MPs who were in Parliament before 1999.
They can use the money to fly to any destination on any airline - the calculation determines how much can be claimed.
Legal blogger Graeme Edgeler has estimated that the change, which now looks unlikely to progress, could increase the maximum rebate from $11,000 to about $20,000 a year.
In response, National MP Simon Bridges said it would take only one objection from a party to ensure his Supplementary Order Paper did not proceed.
And today that objection was confirmed by the Greens.
""The Green Party cannot support a change that has a real likelihood of increasing travel rebates for MPs elected prior to 1999 and their spouses," said co-leader Metiria Turei.
"We can't see any good reason to move away from specifically tying the value of the rebate to the lowest cost option."
Ms Turei said the Government had not provided any analysis of the impact of the cost of their proposed changes, or justified their assertion that they were fixing a mistake.
"Without additional information on those two things, we can't support the changes."
The proposed change had the support of Labour's Annette King, who said it was designed to fix a mistake in the current legislation.
The fare rebate had been pegged to the lowest fare on Air New Zealand since the 1970s, Ms King said.
A mistake in wording saw that change when the long-standing entitlements were transferred to the new Members of Parliament (Remuneration and Services) Act 2013.
"They inadvertently left out 'Air New Zealand', which had always been the benchmark for deciding what the travel entitlement was," Ms King said.
"On July 1 every year, Parliamentary Services go online and go to Expedia I think, and they look for the lowest cost airfare, and [the rebate] stays at that for the year. It has always been benchmarked with Air New Zealand."
Because of the mistake the maximum rebate had most recently been pegged to another airlines' fare, Ms King said.
