The bulk of the nearly $12 billion that the Consumer Financial Protection Bureau has returned to financial customers is attributable to one of the agency's powers that Republicans most want to rein in, according to a new report from House Democrats Monday.

Since opening in 2011, the bureau has won $10.8 billion in consumer relief through enforcements undertaken under its broad authority to police "abusive" conduct in the financial industry, according to the report released by the Democratic staff of the House Financial Services Committee. The bureau verified the statistic.

Under the Dodd-Frank law that created it, the bureau has broad authority to crack down on "unfair, deceptive or abusive acts and practices."

Monday's report makes clear how central that power is to the controversy over the bureau. Republicans have charged that the authority gives the agency free rein to punish businesses for whatever reasons it choose, and they have targeted the power for elimination in legislation that would overhaul the bureau and dramatically scale back its powers.

House Democrats released the report Monday detailing the bureau's accomplishments in an effort to defend it from Republicans.

According to them, the bureau has carried out 129 enforcement actions under its authority to police deceptive or abusive practices. Those include instances such as banks tricking customers into incurring overdraft fees, mortgage lenders engaging in false advertising, and similar complaints against credit score companies, payday lenders and other financial institutions.

The $10.8 billion figure includes not just money that the bureau has returned to customers, but also actions that resulted in the customers having their debt canceled or their balance reduced.