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The incident happened during the lunch break in the ongoing second Test against India.
Pietersen posted the footage on his Twitter feed.
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It shows ground staff member Shane Doherty dragging his right foot as he walked down the centre of the wicket.
India was batting at the time.
Doherty did not appear to be wearing spikes or studs on the bottom of his shoe, so damage to the wicket was far from severe.
However the incident comes amid growing criticism of the Lord's wicket, which has been dry and lifeless in recent years.
But MCC insisted nothing deliberately untoward had taken place.
"MCC admits a genuine, honest mistake -- and there was no intent to damage the pitch," the club said in a statement.
Former England captain Alec Stewart, commentating for the BBC at the weekend, said many English Test wickets needed to be excavated and replaced.
He argued that all wickets had a shelf life of about 20-25 years, and that most England pitches had not been re-laid since the 1970s or 80s.
Stewart said fresh wickets would see the return of the bounce and swing synonymous with UK conditions.