Claimants earning above the permitted limit made up 58% of new overpayment cases last year.
Other reasons for overpayments include the claimant no longer providing care, for example if the person being cared for has died.
Some 136,730 people had outstanding overpayment debt last year, an increase of 71% compared with 2018/19.
However, the NAO said the average value of new overpayments identified by the DWP had fallen in the past four years, suggesting they were being identified earlier.
The DWP seeks to recover all benefit overpayments where it has a legal basis to do so, unless it would cause financial hardship or would not be cost effective.
The department can also refer a case for prosecution if it considers an overpayment was fraudulent, which happened in 54 cases last year.
As an alternative, it can offer an "administrative penalty" of £350 or 50% of the overpayment, whichever figure is greater, up to a maximum of £5,000.
The number of administrative penalties has fallen significantly in recent years, from 774 in 2018-19 to 75 in 2023-24.
Meanwhile, there has been an increase in the use of civil penalties of £50 - with 30,129 imposed last year, up 50% from 2018-19.
The government-ordered review, which will look at how to reduce the risks of overpayment and how to support carers who have already accrued debts, is due to report back by next summer.
Hannah Walker, chief executive of Carers UK, said any recommendations from the review should be implemented as soon as possible.
Dominic Carter, director of policy and public affairs at Carers Trust, called for a "complete overhaul" of the allowance system, describing it as "overly complicated" and "outdated".
Minister for Social Security and Disability Sir Stephen Timms, said: "This report sets out the scale of the challenge and underlines the importance of our independent review into overpayments so we can make the system fairer for thousands of selfless carers.
"Carers deserve to be supported, which is why we are boosting the earnings threshold, benefiting more than 60,000 people, while our review will get to the bottom of the problem so we can protect carers from unfair debt and protect taxpayers' cash."
