The bungled Centrelink debt-recovery controversy has again come under fire with a Perth woman claiming she was hounded to pay back more than $26,000 she allegedly didn't owe.

The Turnbull government is in the midst of trying to recover $4 billion believed to have been incorrectly paid to welfare recipients using Centrelink's new automated data matching system.

A Perth woman claims Centrelink said she owed $26,000.

More than 17,000 debt notices were sent out by the Federal government over the Christmas break, with hundreds of people around Australia complaining they were wrongly hounded for repayments.

Following the litany of complaints, Commonwealth Ombudsman Colin Neave said he would investigate the automated data-matching processes being used to check welfare recipients' eligibility for some Centrelink payments.