Grammar question: Usage of regret

[Monica]

Hello. I'm checking a book on the grammatical usage of "regret". There is the following sentence:
I regret (the fact) that she has left
The book says normally we can omit "that" after regret. But, in my opinion, "I regret she has left" sounds funny. So am I wrong or is the book wrong? Or is simply the example that doesn't work? Thank you

[Mister Micawber]

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'That' can be omitted. The sentence is clear to me without it.
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Native English teacher at Mister Micawber's