Thanks for the explanation. I was actually referring to your sentence, the second part in particular. I can't understand how it's related to the first part. I mean the wording.
OK ... I'll try again. I thought I had it all covered.
The first clause means "By the time this sentence appears as a report". Forget about this being a grammar exercise. This is a sentence that purports to report a past event. Thus it's establishing a time frame. That may be unnecessary, since most people know what reported speech is.
So, let's change it to "in reported speech".
The second clause means that the specific party we are talking about (
which party it was) is already known to the hearer. As I said above, the sentence can't be used until this is established. For example, I can't just say to you, "Mary didn't enjoy the play". That's meaningless to you unless you know who Mary is and which play we're talking about. So prior to saying that, I have to let you know who and what I'm talking about.
Hence, by the time it's reported in this way (Mary didn't enjoy the play), you will already know which Mary and which play I'm talking about - by the pragmatics of language use.
Hence similarly, "By the time it's reported in that way, which party has already been established."
In reported speech certain parameters must already have been established before you can use a sentence such as the index sentence we are discussing. One of those parameters that is known already is which party we are talking about. Hence "
the party" is sufficient in reported speech.
If it's my use of "which" which is worrying you, note that I've italicized or bolded it both times. It's stressed.