TSB's online banking meltdown is being investigated by the Financial Conduct Authority, the regulator said on Wednesday as it revealed more than 10,000 customers had been defrauded.
The computer failure in April after the introduction of a new IT system led to 1.9m customers losing access to internet banking. Many are still struggling to access services.
In a letter to parliament's Treasury committee, FCA chief executive Andrew Bailey said he had been "dissatisfied with TSB's communications with its customers and we have had concerns that TSB was not being open and transparent about the issues experienced".
"The current communications were perceived as poor, and could reduce trust in TSB and in the banking sector as a whole," he said, adding that TSB chief Paul Pester had given an "optimistic view" of services.
"We do not normally make this information [the investigation] public, but, given the level of public interest, I want to be clear that we will be conducting this work," Bailey added.
In later live evidence before the committee, Bailey revealed more than 10,000 customers had also been defrauded as a result of the failures.
"I"m going to be a little bit circumspect about what we say about fraud...as we don't want to give information that fraudsters could use against the firm. We think there's been just over 10,000, 10,600, incidents, and that has resulted in a level of payout."
Pester also faced a second grilling in front of MPs from the cross-party Treasury committee on Wednesday.
Bailey revealed in his letter that 40% of telephone calls to TSB were still being disconnected or abandoned and if customers did manage to get through they faced a 30 minute wait to speak to bank staff.
He also said that there had been an increase in fraud after the IT changes "over and above the anticipated rise in fraud estimated by TSB ahead of the migration".
"This Is a continuing area of concern for the FCA," Bailey said.
"We are in close contact with TSB In relation to fraud and have made It clear to TSB, with which they concur, that no customer should lose out as a result of the problems at the firm and that we expect TSB to quickly resolve any reports of fraud."
"We have been clear that TSB needs to be doing everything It can to support customers who have been a victim of fraud and put them back Into the position that they would have been In, If the fraud had not occurred."