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 follow up to confirm an invoice contact, use this factual base: summarize the deliverable, version, requested input, owner, and effect on the schedule.
Correct the record precisely
Correct only what you can support, acknowledge any real impact, and propose a practical way to prevent repetition. Give a small set of options and explain which default plan applies if the real deadline passes. 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 bury a scope or price change, threaten the relationship, or pretend silence means approval. Use the contract and documented escalation route for legal, payment, privacy, or security decisions. Do not recruit an audience, publish private evidence, or turn a misunderstanding into a campaign about character.