The intermediate compressor problems, and earlier turbine blade problems, led to groundings and severe disruption for airlines, including Thai and LATAM which also serve this market.
British Airways, Virgin Atlantic and Singapore Airlines' regional carrier Scoot have also been affected by problems with Trent Package C engines, used by about 25 per cent of the Dreamliner fleet.
Air New Zealand is gradually getting its repaired engines back into service but will lease two aircraft - which it can crew with its own staff - to help give it more flexibility through the winter.
Yesterday Portuguese wet lease operator Hi Fly — which supplies aircraft and crew — was due to have flown its final Auckland-Honolulu flight for Air New Zealand after supplementing services on the route for the past three weeks.
One of the next leased planes will be a Singapore Airlines Boeing 777-200ER which is registered on the New Zealand Civil Aviation register to allow it to be staffed by Air New Zealand pilots and cabin crew.
The Rolls-Royce spokesman said the engines were generally repaired in the order that they arrived at the company's bases in Singapore and Darby, England.
''However we do recognise there are some airlines that need certain things in order for them to fly - we've been juggling that around a bit to help airlines that are badly affected,'' he said on the sidelines of the International Air Transport Association meeting in Sydney last week.
Rolls has said that the cash hit from the Trent problems should hit a peak of £340 million (NZ$648m) in 2018 before falling in 2019.
The cost of the extra inspections would be covered by cutting discretionary spending elsewhere, including cutting travel, training and non-urgent information technology projects, the spokesman said.
Airlines generally buy care packages at the time they buy the engines and allows them and Rolls to come to an agreed settlement if there are problems which ground them. It gets more complicated when there are exceptional costs, such as wet lease fees.
Air New Zealand's most recently delivered aircraft have Trent 1000 TEN engines that are not affected.
In April a US Federal Aviation Administration airworthiness directive detailed potential risks from faulty compressors and also restricted the distance aircraft with the affected engines were able to fly from alternative airports.
The FAA directive meant before checks and any repairs they could not fly further than 2 hours, 20 minutes from an airport, down from five-and-a-half hours.