Of the two choices, the simple past is best (although not "official!")
She said she would collect the book on Monday when she came home from school.
Irrealis conditionals like would call for this kind of tense simplification in subordinate clauses. We use the preterite came here because at the time in the future when the subject will collect the book, the action of coming home is already completed.
In Swan's Practical English Usage, the author says:
If the main verb of a sentence makes it clear what kind of time the speaker is talking about, it is not always necessary for the same time to be indicated again in subordinate clauses.
Would, like will, is avoided in subordinate clauses; instead, we generally use past verbs. This happens in if-clauses, and also after most other conjunctions.
Contrast your example with the same sentence using the simple future instead of the conditional:
She said she will collect the book on Monday when she comes home from school.
Here the verb in the WH-clause is simplified to the simple present.