Carrot Insurance - which aims to make car insurance policies more affordable - relies on data to measure journey length, acceleration and braking, but according to some consumers, the app hasn't been working as it ought to have.
Carrot has already issued an apology, saying it was "extremely sorry" that some of their customers had a "poor experience" with the app.
However, the company has defended its track record, insisting that "for the vast majority" of young people, Carrot had actually helped to reduce their costs.
Carrot markets its Better Driver app as "a clever bit of technology which uses 'telematics' to measure acceleration, braking, swerving, and the number and length of journeys that you make".
The technology is designed to reward users for good driving and is geared towards helping younger drivers, who have historically had to pay higher prices.
Carrot has told the BBC that it has either already compensated "all those customers" who have alerted them to the issue, or the firm is currently investigating any unresolved cases.