Police are carrying out inquiries into Lord Mandelson and Andrew Mountbatten-Windsor's links to sex offender Jeffrey Epstein.
While the trip is not officially confirmed, the King and Queen Camilla are reportedly planning to visit the US at the end of April.
They are understood to have made "alternative plans" instead of joining the Royal Family in Windsor.
An MP says the Freedom of York award must be scrutinised after it was stripped from Sarah Ferguson.
The letter, seen by the BBC, also called on Ferguson to share any knowledge about Andrew Mountbatten-Windsor's links to Epstein.
The former duchess was given the honour in 1987 following her marriage to the then-Prince Andrew.
The paving slab near the council offices on Parliament Way has now been replaced – or turned over.
The plaque had marked Mountbatten-Windsor planting a tree in 2009 to commemorate the city's 400th anniversary.
The Corporation of London is of the view that it cannot rescind the ex-prince's Freedom of the City.
