した in 会話した is simply a part of the suru-verb 会話する ("to converse"), which is an intransitive verb that does not take を.
If we took this こと after 会話した as a nominalizer, this would mean "She writes even the fact her classmates conversed", which makes almost no sense to me. The mere fact that "students made a conversation" is not a meaningful piece of information because students do so every day.
So I think this こと simply is "things", and 会話したこと means "the things we conversed about", or "the contents of our conversations".
Relative clauses in Japanese can have an adverbial relationship with the modified noun (Type B in this question), and can be safely used with intransitive verbs.
- よく行く場所 the place we often go to
- 何か書くもの something to write with (eg, a pen)
- 何か書くこと something to write about (eg, an event)
- 感謝の気持ちを表す言葉 words with which I can express my gratitude