One customer was told that clients who had not paid would not be required to do so and those who had would receive a refund.

The bank on Wednesday denied the move was part of a broader refund or abandonment of the fee.

"We are aware that for a small number of clients, some Commonwealth Private advisers have chosen to make a goodwill payment on a case by case basis," a bank spokeswoman said.

While the other retail superannuation funds run by the big four banks are also passing on some of the costs of regulation, the fees on wrap products at CBA and Westpac-owned BT are the highest in the market. Wrap products are superannuation platforms that let members or their advisers directly choose investments.

The $40 fee at FirstChoice is similar to other retail funds - except for NAB, which does not currently charge a fee of this kind on any super product.

Misconduct at Commonwealth Bank's wealth management and insurance businesses is part of the reason the Hayne royal commission into the financial services sector was established.

The Productivity Commission this week released a report taking aim partly at the level of fees charged on superannuation accounts.

Ms O'Dwyer pointed to this again on Wednesday when asked about the partial refunds.

“The government is concerned about the fees imposed by superannuation funds, which is exactly why we announced in the budget a cap on administration and investment fees, banning exit fees and stopping inappropriate insurance premiums," she said.

The original letter states customers with multiple accounts will only be charged once, while accounts with balances below $5000 or holding only suspended investments will not be charged. The fee charged by Commonwealth Bank is on top of existing administration and investment fees.

In the original letter to super members, Commonwealth Bank had blamed a number of "highly technical and complex" regulatory reforms for the fee hike.