Orbitz review: Hotel reservations error by agent

Orbitz refuses to acknowledge an error made by a booking agent that cost my friend and me $502. for one night stay at a hotel we did not have.
On July 14, 2021, I made hotel reservations with Orbitz for 3 nights in Geneva and 2 nights in Zurich; October 1, 2, and 3 at Hotel Suisse in Geneva and October 4 and 5 at Hotel Schweizerhof in Zurich.
On September 9th I phoned Orbitz to change the reservation to 4 nights in Geneva (10/1, 10/2, 10/3 and 10/4) and 2 nights in Zurich (10/5 and 10/6). The agent mistakenly booked us for 3 nights in each city. Arriving in Geneva, we were surprised that our booking was for just 3 days, but we paid for the extra night. In Zurich, we were told that we were expected on October 4 and in order to stay we would have to pay $502.
Back in the States, I contacted Orbitz for a refund, was told by Yvette M/SALIcedillos in customer support to email a copy of the Hotel Schweizerhof invoice, which I did. Orbitz's solution was to request a refund from the hotel on my behalf. Of course it was denied. The hotel was not in error.
I have spent the last 2 weeks, via phone calls, emails and chats to get this refund and have been met with inconsistences, excuses and even lies by agents. I have read countless reviews in which victims of Orbitz's practices have made similar complaints. Something should be done. My itinerary # [protected]. I will try to attach a copy of the email from Orbitz wherein lies the mistake.

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