If they did not give you any contact information, I would contact Wal-mart's legal department. You do not have to pay this. If this is just a civil demand, they would still have to take you to court and prove their case in order to make you pay. It may be a case of mistaken identity. If do sue you, you may wish to consult with a civil defense attorney.
You are under no legal obligation to pay Walmart's demand. Feel free to peruse our blog regarding petty theft and these demand letters.
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A civil demand letter does not create an obligation to pay unless it is follow by a civil lawsuit which almost never happens.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
Ignore it. Better still, call them and tell 'em (politely) to POUND SAND.
Law Offices of Jay S. Finnecy (619) 855-3003 or (760) 522-7006 criminalattorneysd.com
Ignore, but hold onto, the letter. If you do not truly recall this incident, you should have an attorney look into this for you.
Law Offices of David Shapiro 3555 4th Avenue San Diego, CA 92103 (619) 295-3555
A civil demand letter does not create an obligation to pay unless it is follow by a civil lawsuit. I would keep a file and see if anything else happens. If it does then you go from there. But otherwise, just keep a file.