Current BBC "English"

(Introductory note: I expect that more than a few readers who happen on this topic frequently won't even understand what the posts' points are all about.)
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topic/subject in text on the screen beneath a pictured interview

"What do I tell the boss about me returning to work?"

(i.e. the pandemic of Covid-19's post-quarantine)

That misconstruction is so commonly written that I stop and look twice when I actually see the possessive. Sometimes I think the editors are introducing the errors (the cardinal sin of editing).

When I hear the correct construction in speech, it affects my estimation of the speaker.

I'm in the U.S. I'm sorry to know this is happening with the BBC.

True enough. And the example shows us the problem with numerous such sloppy cases of usage--for the phrase may be variously interpreted:

Correct forms:

What should (ought) I tell the boss about my return to work?

What ought I tell the boss about my returning to work?
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confused variants:

Upon my return to work, what do I tell the boss? About me?

What do I tell the boss about? Me? Returning to work?

What? Do I tell the boss about me returning to work?

What? Do I tell the boss? About me? About returning to work?

What do I tell? Returning to work, the boss about me?

What? Do I tell? Returning to work-- the boss about me?

"What do I tell the boss about returning to work?"

Is the clearest. There's no need for a pronoun, unless it becomes ambiguous, which is usually handled from context.