A carve out is a simple compound, and typically a verb, but can be used as a noun as seen above. It notes an exception (typically to a policy, practice, or law)

caveat /ˈkavɪat/ noun

a warning or proviso of specific stipulations, conditions, or limitations. ‘there are a number of caveats which concern the validity of the assessment results’

Emphasis mine.

I understand now the purpose of it. Normally in non-americanised English, using your example, caveat is used as follows:

“The deal has a caveat that x gets y” where caveat covers both meanings.

But that’s been Americanised because you’re separating those meanings effectively saying “There’s a caveat, the caveat is x gets y” as, “There’s a caveat, the carve out is x gets y”.

So, it isn’t that your TV personalities couldn’t speak, it’s because your contract writers were semi-literate.

What were you saying about my English competency?