The word "wouldn't" is correctly used here, and is the preferred form. Because this is indirect speech it is back-shifted from the present form "won't" to the past form "wouldn't". Anna probably said something like "I won't be home until eleven" in the telephone call, but this is altered when it is reported using indirect speech.
If the absent speaker's speech is quoted, instead of being described using indirect speech, it is not back-shifted. For example:
- Iris: She called me before dinner and said "I won't be back until about eleven"
- Iris: She left me a message that said "I will arrive tomorrow afternoon".
But notice that when direct quotation is used, the pronoun is also unchanged; it remains "I" although it refers to Anna, not to Iris.
When Iris starts her sentence "She said that she ..." she is using indirect speech, and will often back-shift the reported statement, so
Iris: She said that she would come back tomorrow.
Iris: She said that she will come back tomorrow.
However, particularly when the reported situation has not changed, back-shifting may be omitted. This means that the original example using "will" is not wrong although it is the less common usage.
As The Cambridge Grammar of the English Language says on pp. 156–157), when the reported speech is recent and the situation has not changed, the change from a back-shifted to a non-back-shifted form "will not affect the validity of the report in any way". It says further that when the original is in the preterite perfect ("I had left") back-shifting is not possible. In all other cases, it says, back-shifting is the default option and gives a more faithful report of the original speech, because it looks at things from the same point in time as the original speaker. The book goes on to say that a non-back-shifted form indicates that the original statement is still applicable and relevant
Note that when the reporting verb is in the present tense back-shifting is not used;
She says that she will be home by eleven
but this is not true when the reporting verb is in any past tense, as in the examples in the question:
She said that she would be home by eleven
In this case back-shifting will often be done.
Consider a case where a recent speech is reported, and the situation has not changed:
- The radio said that it would be sunny tomorrow.
- The radio said that it will be sunny tomorrow.
- The radio says that it will be sunny tomorrow.
I personally would use the fist or third of these, not the second, and I think that the majority of fluent speakers would do so more often than not. But the second form is not wrong, and some fluent speakers use it routinely.
As fluent speakers do not always use back-shifting, even when the "rules" would favor it, and as English has few if any hard-and-fast rules, my original answer was incorrect in saying firmly that the use of "will" in the original example was wrong.
For more details on back-shifting in English see: