If you use a company travel agent, they usually / often have "side deals" with the employer so there are additional incentives / discounts / paybacks that are invisible to the employee, and the price you see, or your travel cost centre budget is charged is not necessarily the actual price paid.

For example: I was caught out a few years ago when my employer started to use Concur, and we were "strongly encouraged" to use them for all hotel bookings. It took me a time to realise that the price shown to me was exclusive of hotel points for membership purposes and so I wasn't getting benefits from the stays. Even though the price was the same as the hotel website and app.

I think the general rule is: if you buy through a TA then only the TA can make any changes until it comes under airport control. They are the rules.