The accusation has been made in court documents and puts the figure at more than double the original estimate.
The group, which includes Massachusetts and Connecticut Bankers Associations, claims 65 million Visa account numbers and 29 million MasterCard account numbers were stolen.
The legal challenge includes sealed testimony from the two credit card companies and Visa has already estimated its losses at between $68m-$83m (£33m-£40.5m).
TJX originally calculated its losses at $12m.
However, in September this year the company agreed to settle a series of class-action lawsuits by customers, bring its total losses from the data breach to roughly $128m.
The problems occurred over an 18-month period covering 2005 and 2006 at the company's database in Massachusetts.
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