"I can absolutely guarantee you that many of their primary APIs are literally screen-scraping terminal sessions and returning the screen as XML"True, but TPF is scalable enough that it doesn't matter. The API is responsive, flexible, and handles the traffic. The ugliness isn't limiting new functionality, etc.
We spend very little time talking about the cruft at the bottom. The business complexity is more important.
Things like fare classes, discount codes, availability, fare basis codes, reaccommodation, and so forth. If it were all written in rust or Go + microservices it wouldn't be any more straightforward.
Your product seems to confirm that. You aren't reducing that screen scraping any. But you're adding value.