Cheltenham Borough Council has said the authority had ordered the owner to carry out "urgent works" on the house.
They were designed to stop further deterioration of the listed building, make it weatherproof and stop the risk of falling render.
Mark Nelson, enforcement manager at the Borough Council, said removing any pieces would be classed as a criminal offence.
We have endeavoured to protect the Banksy as much as possible and to this end the notice required the owner to have due regard for the Banksy mural whilst works were being undertaken.
We were aware of loose render on that part of the building where this was situated but the extent and how far it would affect the mural was unknown until work progressed.
The owner has left pieces of the render with attached Banksy Spy Booth mural on it with the council whilst investigations are continuing.
We would advise anyone against removing any further pieces from the location as this may be classed as a criminal offence.
Until the investigation is complete we are unable to say what if any further action will be taken.
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A 22-year-old man has been taken to hospital after he was stabbed multiple times in the chest.
The serious assault happened in Cheltenham town centre during the early hours of the morning, and a 21-year-old woman has been arrested in connection with the incident.
The incident happened at a home on Devonshire Street in Cheltenham at around 3.45am this morning.
The High Street is closed in both directions between Gloucester Road and the Royal Mail building while police investigate.
A statement from Gloucestershire Police said:
The offenders are believed to be three black men who left the scene in a silver Citroen 'bubble shaped' car.
One was of a large build and wearing a white vest top, one had dreadlocks. We understand this will cause concern within the local community but we wish to reassure residents that this is believed to be an isolated and contained incident.
A 21-year-old woman from Cheltenham has been arrested on suspicion of assisting an offender and drug supply in connection with the incident."
Anyone with information should call police on 101.
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The students from Cheltenham Bournside School were rushed to hospital on Saturday after the coach they were on crashed.
The school released a statement today which said:
"We are delighted to be able to share that each of the two students who were seriously injured in the coach crash on Saturday are making very good progress and hope to be flown home over the next couple of days."
"Both families would like to thank everyone for their support to date and for their kind words on social media, which has been of great comfort at such a difficult time."
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