Seek prompt review using the actual records and identify relevant work, stay and travel dates. Do not ignore the difference or decide its legal effect from a guess.
Use the appropriate record-specific response
The issuing authority and circumstances matter to any correction or other step. Keep accurate copies and obtain guidance on the actual process before relying on the disputed date or classification. Two clocks run once a discrepancy is spotted, and both should be identified before a response is chosen.
One is the operational date: the flight, the start date, the payroll cycle. The other is the date on which the applicant's permitted stay or work authorization actually depends, which is the one carrying legal consequence. Where the second is comfortably distant, the right step is usually to obtain a considered answer and move the operational date.
Where the second is close, the question changes into what the applicant must stop doing while that answer is obtained, and that is a decision to take deliberately rather than by default. State both dates when raising the issue. A reviewer given only the flight date will optimise for the flight, which is rarely the thing that matters most.
Where the two dates cannot both be met, decide which one moves before the week begins; a choice deferred until the day before departure is usually made by circumstance rather than by anyone in the file.