Benefit claimants must inform the Department of Work and Pensions if their bank balance exceeds £16,000, either due to a windfall or inheritance.
However Banana, who appeared on the Channel 4 show hosted by Noel Edmonds in November 2011, did not disclose her winnings.
She admitted failing to disclose her windfall separately to both the DWP and Stoke City Council with the intention of making a gain between March 28, 2011 and May 13, 2012.
The council said in all she had been overpaid about £7,200 in housing benefit, council tax and income support.
She also admitted failing to declare to the DWP and the council her employment at a chemists, medical surgery and Longton Cottage Hospital.
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'I am immensely proud of the officers involved and want to thank them for their bravery in bringing this incident to a safe conclusion.'