In a Facebook post, Greig said the National Trust should not waste money on restoring a stately home which was built using profits made in the slave trade.
The criticism comes after design teams were invited by the National Trust to submit plans for the £30 million project on Thursday.
Clandon Park was built in 1733 by politician Thomas Onslow. Onslow owned 2,000 acres of plantation land in Jamaica where he produced sugar. He voted against the abolition of the slave trade in 1796.
The 18th century mansion was gutted in a fire in April 2015. The blaze destroyed more than 90 per cent of the building's roof and interiors.
Greig criticised the Trust's decision to spend money on the restoration of the property.
The ancestral owner of the property told the Telegraph he thought the Trust should not rebuild the property.
Rupert Olslow, the eighth Earl of Onslow told the newspaper: "The building is dead and I think it's wrong to try and rebuild it. The result can only ever be a copy, a pastiche. I've no doubt it would be a beautiful copy, but it would be a copy nonetheless."
A spokesperson from the National Trust told Premier:
"We recognise that Clandon was built partly with money inherited from Elizabeth Knight's uncle, who profited from the slave trade. We have never shied away from acknowledging this aspect of Clandon's history and our research is ongoing. When considering interpretation for Clandon in the future, we will continue to explore its links to the slave trade and other important aspects from its 300 year-old history.
"The house is architecturally and historically very significant and this is recognised in its grade I listing. Clandon was given to the National Trust by the Countess of Iveagh for us to preserve, protect and share, so we have a legal and a moral obligation to preserve the house's significance. In addition to this, the restoration of Clandon will be funded by insurance money, which can only be used at Clandon and not spent elsewhere."