Make room for the other version
Ask what the other person understood before assuming that you are arguing about the same facts. For a message about how to invite someone to an apology conversation, use this factual base: give the event, date, location, relevant history, and what kind of contact the invitation involves.
Correct the record precisely
Correct only what you can support, acknowledge any real impact, and propose a practical way to prevent repetition. Offer a simple way to accept, decline, ask a practical question, or choose a lower-contact option. Make the immediate next step clear enough that the recipient can answer without reconstructing the entire history.
Agree on a testable next step
Do not announce their attendance, use relatives to persuade them, or make a public gesture before they agree. Respect no-contact, venue safety, custody, and legal restrictions even when the event feels important. Do not recruit an audience, publish private evidence, or turn a misunderstanding into a campaign about character.