Co-leader Metiria Turei said the proposed change "has a real likelihood of increasing" the travel rebates.
Former MPs who were in Parliament before 1999 are able to claim an international travel discount for them and their spouse each year, paid for by taxpayers.
The maximum rebate is recalculated every year by Parliamentary Service, whose staff look up a current airfare to base it upon.
Since the 1970s that airfare has been specified as an Air New Zealand business class return fare from Auckland to London.
But that changed to the lowest-cost business airfare available after the new Members of Parliament (Remuneration and Services) Act 2013.
Omitting the Air NZ specification was a mistake, the Government said, and this week's amendment will fix that.
Because Air NZ is often not the cheapest option, legal blogger Graeme Edgeler has estimated that the change could have increased the maximum rebate from $11,000 to about $20,000 a year.
However, figures provided by Parliamentary Service show that for 2014/15 - the first year an airline's fare other than Air NZ was used - the cap was $12,414.
In the previous financial year - when Air NZ had to be used as the basis for calculation - the cap was similar at $11,850.
Former MPs can use the money to fly to any destination on any airline - the calculation determines how much can be claimed.
Their spouse is entitled to the same allowance.
Yesterday Prime Minister John Key said the Government was unlikely to press ahead with the change after Mr Bridge's amendment was defeated.
Asked if the perks should be removed altogether, he said they were set long ago and were now limited to MPs in Parliament before 1999.
"Generally retrospective legislation is not a good thing."
MPs' Travel Perks
• Date back to 1972 and give former MPs and their spouses discounts on international travel up to the value of a business-class return trip to London. They also get 12 return domestic flights a year.
• The level of travel discount former MPs receive increases the longer they were in Parliament, up to a maximum of 90 per cent for those who serve five terms or more.
• The cap for the international travel rebate for 2014/2015 is $12,414 - or $11,173 for those entitled to a 90 per cent rebate ($22,345 per couple).
• Current MPs who will get a 90 per cent rebate when they leave Parliament are Peter Dunne, Ruth Dyson, Bill English, Phil Goff, Annette King, Trevor Mallard, Murray McCully, Damien O'Connor, Winston Peters, Nick Smith, Maurice Williamson.
• Those who would currently qualify for a 70 per cent rebate if they left are Gerry Brownlee, David Carter, Nanaia Mahuta, Ron Mark.
• Only former MPs elected prior to 1999 are still entitled to the travel perk. When he leaves Parliament, Prime Minister John Key will be eligible for taxpayer-funded domestic travel where the travel is undertaken in his role as a former Prime Minister.
