Gotogate Charged Me $54 for a Free Flight Change

I booked Istanbul–Tokyo tickets through Gotogate for my family of four, including two children. The order number is 1120-562-399, the PNR is pepngn, and the carrier is China Southern.

July 4: The airline canceled our return flight. Gotogate proposed a 35-hour layover itinerary. I rejected it and requested CZ648/CZ679 instead.

Because the cancellation was caused by the airline, this change was free of charge under the carrier's rules. Gotogate never informed me that I was entitled to this option.

July 22: They requested a $54 “service fee.”
July 24: They confirmed in writing that “yes, the flight information is correct.” I made the payment the same day.

However, the change had not actually been processed.

August 15, one day before our departure: They wrote that they “had not yet received the necessary authorization from the airline” and suggested that I contact the airline myself. I contacted both companies that same day. China Southern responded within hours; Gotogate did not.

August 16: The airline confirmed in writing that our return flights were showing as NO4 in the system, meaning they had not been ticketed, while the outbound flights were showing as HK4, meaning they were confirmed. They also stated that the flights “should be eligible for a free change due to the flight cancellation.”

August 18: I called the airline myself. China Southern processed the change directly, without charging me a single penny, and issued all four tickets under new ticket numbers.

August 19 at 4:44 AM: Gotogate was still saying that they were “waiting for the airline's approval.”
August 19 at 8:13 AM: That same morning, they sent me an email stating that “your itinerary has been updated.” However, the ticket numbers in the email were the old numbers that had become invalid the previous day. If Gotogate had actually processed the change, they would have known the new ticket numbers.

August 19: I requested a refund and gave them 14 days to process it. The only response I received was from an automated bot.
September 12: After 24 days, they replied to an earlier message stating that “your flight has already taken place and the services have been resolved.” They did not mention the fee they had charged me at all.

In summary, they failed to inform me about an option that should have been free, charged me for it instead, represented the change as completed when they had not actually processed it, and left a family with two children without valid return tickets for six weeks.

My request is simple: I want a full refund of the $54 service fee. I have all of the correspondence and supporting records.