Undercover police were alerted to the woman's behaviour, with reports she attempted to break-in at the South London school on September 12. She was arrested shortly after.
Royal protection officers were alerted when the woman turned up unannounced in the school's reception area, before fleeing when challenged by staff. She then returned to the school vicinity the following day.
While the woman was initially arrested on suspicion of attempted robbery, she has now accepted the caution for 'causing nuisance on school property' under the Education Act.
'A 40-year-old woman has accepted a caution for causing a nuisance on school property following an incident at Thomas's Battersea school in September,' London's Metropolitan Police statement read today.
Prince George, who is currently attending reception classes on a half-day basis, until lunchtime, was not present at the time of either incidents.
This article originally appeared on New Idea.