A question about とはいえ

In both the about section and some examples, the ‘は’ is sometimes omitted as is ‘だ’ after some nouns.

Is this natural and the explanation simply needing notes about exceptions or are these typos?

The だ after nouns seems to be optional. At least it’s in parentheses in the grammar structure:

Whether は is optional or not, I don’t know.

I asked ChatGPT and the answer seems confident, but as always may be made up:

Yes, といえ (to ie) is a shortened form of とはいえ (to wa ie). Both expressions mean “having said that” or “that being said” and are used to introduce a statement that contrasts with or provides an exception to what was previously mentioned.

といえ: a more casual, conversational form.
とはいえ: a more formal or complete form, often used in written language.



Both sentences mean “It is raining. That being said, I have to go.”

Thanks, I probably should have noted that about だ.

It seems to have happened too many times with は, I just expected a heads up.