The commission ruled in March that the Diocese of Guildford, the sole trustee of the Dunsfold Church of England School Trust, could lease the school in Dunsford, which has been empty since 2004.
The commission's decision changes its earlier decision in 2009 that the diocese could sell the building. The change followed objections by local residents.
A group of four local residents, including two members of Dunsfold Parish Council, has now asked the charity tribunal to review the decision to let the diocese lease the building.
The commission said in its decision in March that the issue was controversial and that the local residents wanted the building to be brought back into use as a school.
"There was a strong feeling that the premises should be retained and not sold off," it said. "The general view was that if this site is lost it will not be possible to provide a school in the village in the future."
The commission's ruling said the school building had to be leased to an organisation that would use it for educational purposes, with any profits used to fund the education of local children.
None of the claimants were available for comment.