Your corrections
The suggestions you saw in conversation do not disappear; they collect in a list.
Where it lives
On that phone only. It is not sent to us and it is kept out of backups. You can delete entries one by one or all at once.
Not behind the paywall
Your corrections, what the other person knows about you and your session summary never require a subscription. That is one of the product's founding decisions.
The other person does not bring it up
A mistake in the notebook is not thrown back at you in conversation. The suggestion is shown once, then the conversation goes on.