Telecom Retail Media & PR manager Lucy Jackson said all cases of suspected fraud were investigated by Telecom's Fraud Team and where appropriate the cases were referred to police.
"Telecom tightened security when it is necessary. Fraud like that described in this instance does occur and so we are continually reviewing our security processes across all parts of our business to ensure they protect our customers and our business from fraudsters," she said.
"We remind staff to be vigilant, balancing that with ensuring a smooth experience for our customers," she said.
Ms Jackson said if customers had an insurance policy with Telecom and wished to make a claim, they should call 0800 MOBINS (0800 662 467) for help.
"If their phone has been lost or stolen, they should contact us straight away so that we can put a bar on the phone and prevent anyone else from using it. When making an insurance claim for a lost or stolen phone, customers must first report it to the police, who will give them a lost property report or complaint acknowledgement form."
Ms Jackson said if a customer is offered a cheap iPhone and they have concerns or questions, they can use Telecom's Phone Compatibility Checker to find out if the device has been reported lost or stolen.
"Alternatively, they can visit a Telecom store and one of our people will help them," she said.
Ms Jackson said she was unable to provide details of the types and quantity of insurance fraud Telecom dealt with.
"We don't want to encourage copycat-type crimes."