I never picked up the Quartet, but if I had I would've scratched my head over the omission of the bonus tracks, since I recall them being (and sounding) very good, and they were presumably available.
As an aside: my copy is in storage, but I distinctly recall "Vitelloni's Bar" being a solid re-recording of the "I Vitelloni" theme (presumably recorded to be used as source music for "Roma," but I don't recall hearing it the last time I watched the movie).
The "bonus" tracks are ruther funny. "Vitelloni's Bar" includes the "Vitelloni" theme as you suggested. The "Aria di Roma" sounds a bit like Rozsa doing Roma Amazing stuff...
I downloaded the album from qobuz. It's mastered very differently in comparison to the Quartet release. Cuetools doesn't recognize it - so it is neither the GDM, nor the Verita Note disk. I just hope it is not a transcode.