So they’re doing it to shout about it rather than being contractual.
It's very unlikely to be contractual. Even the BBC Studioworks credit is unlikely to be a contractual requirement.
"Television Centre, White City" may get an additional credit if the people running the wider site have been particularly helpful - say with exterior items, site security, co-operating with wider site-related stuff etc.
Any on-screen mentions of it, or exterior shots, are purely there from an editorial point of view, to give the show a sense of place etc. (And arguably trading on the heritage of the site as 'the home of British TV')