The authority said on Tuesday (17 December) in excess of £200 million across more than 250,000 claims had been paid out.
Cook collapsed on 23 September.
The refund process had been due to get under way on 30 September but the CAA pushed the process back a week to implement a more robust online claims system to handle what is the single largest refund effort under the Atol scheme in its history.
Earlier this month, the CAA confirmed that approximately two-thirds of valid claims made on the first day of the refund process had been paid within its own 60-day target.
The CAA said the delays were a result of it having to seek additional information from certain claimants ahead of payment.
Cook customers with legitimate claims have until 22 September 2020 to lodge them with the CAA, and the authority has urged anyone with outstanding claims to do so as soon as possible.
CAA chief executive Richard Moriarty said: “We thank consumers for their ongoing patience as we undertake the UK’s largest and most complex travel claims operation.
“We want to ensure we get the right amount of money back to the right people as soon as we can, and we have so far paid out over £200 million by settling over a quarter of a million claims, 75% of the total we have received.
“We understand those consumers who have not been paid yet have had to wait longer than we had hoped and we are doing all we can to process these claims as soon as possible.
“Unfortunately, our operation has had to include extra checks and processes owing to the quality of the information we received from Thomas Cook’s systems and the potential threats of scams and fraud.
“We will continue to make as many payments as possible each day and contact consumers that need to provide us with further information in order to validate their claims.”
