Officials have told the government they are sometimes struggling to identify who needs to pay for their managed isolation stay.
Meanwhile, the total amount earned by the MIQ fees scheme - about $4.3 million for each month it has been in place - falls well short of the expected revenue.
In Cabinet documents from February obtained by RNZ, the Ministry of Business, Innovation and Employment said travellers may be signalling they will be in the country for long enough to get a free stay, then leaving earlier.
It does not know how many people could be rorting the system.
"This is a trust model that may not always reflect people's circumstances, and it is not currently possible to identify whether returnees' circumstances have changed," it said.
"Officials are attempting to address this issue and other data challenges."
The Cabinet documents precede a range of changes being made to the MIQ fees system, including an information-sharing agreement with immigration officials, to help work out who leaves the country within 180 days of arriving and needs to pay for MIQ.
Soon, returnees will have 30 days to pay their bill rather than 90 days, and will be sent their invoices within two weeks of their stay - rather than an average of 43 days later.
Already the government has extended the period people need to stay in New Zealand to be eligible for free MIQ, from 90 to 180 days.
In the documents the ministry sets out the amount it expected to recoup from the fees scheme, telling the government it would get an expected $500,000 more each month when it extended the minimum stay.
"This would increase total revenue to an estimated $15.2 million per month," it said.
However, the total amount recouped by the ministry in 10 months is about $43m - or $4.3m for each month since the scheme was introduced on 11 August.
Another $14.8m worth of invoices have been sent out, but are not yet due.
Meanwhile, about 2000 invoices worth nearly $7m are overdue, from people who left MIQ more than 90 days ago.
Asked why there was such a large gap between the expected revenue and total revenue, the ministry said the $15.3m was an estimate taken from the number of liable returnees expected to come through MIQ each month.
"This was based on the data available at the time ... also based on occupancy levels, people per room and fees-based voucher allocations to different classes of returnees," it said.
"From the potential number of people liable for charges, there will be a portion who are not required to pay as they have a waiver approved, or are exempt from charges under the regulations. In addition, the fees regime has evolved since it was introduced seven months ago and more categories of people are potentially eligible to pay for their MIQ stay."
Asked about those potentially leaving the country before they are eligible for a free stay, the ministry said it was still working through the data from Immigration New Zealand to work out "if this is a problem".
It noted that legally, it would not be able to prevent people leaving the country if they had outstanding MIQ fees.
Because invoices are currently not due for 90 days, it also noted people leaving early would not necessarily have overdue fees.
The ministry said most people wanted "to do the right thing and play their part in the response".
"We are continually improving our processes and expect the amount received from fees will increase," it said.