What your employees (present or former) write in their resume is not your problem. If they apply to a job with false data, it is their problem and the (prospective) employer's problem. Don't worry about it and don't tell them to fix their resume.
The only two scenarios where you could do anything about it are:
If they apply for a job at your company, you can reject their application for providing false data. This also holds if you work for another company in future, and they apply there.
If a background checking agency (hired by their prospective employer) asks you to verify their employment, you can inform them of the discrepancy in an objective manner, such as below:
This is in response to your request for verification of employment dates of Mr John Doe at Acme Corporation. As per our HR records, he was employed with us from July 1, 2016 to July 22, 2016.
Do not call out the employee's lies, just state the facts and be done with. Let the background checker and the prospective employer figure out how to deal with the discrepancy. Stay professional even when others behave unprofessionally.
I feel like our business is being misrepresented, as I know this employee has stretched their employment dates at my business.
Fudging employment dates, exaggerating achievements, introducing fictitious employers and awards, and writing other
creative lies metaphorically true statements in the resume happens frequently enough that there's a term to describe it: resume padding. Everyone understands that it is impractical for any employer to police what their employees write in their resumes. No reasonable employer would hold that against you.