Charities opposed the clause because they felt they did not have sufficient control over volunteers to comply with it.
The FSB has also scrapped requirements for charities to train volunteer fundraisers in the Institute of Fundraising's codes of practice and the board's Fundraising Promise.
Instead, charities must provide volunteers with guidance on the codes and promote the scheme to them "where practical".
The amendments were made after the institute convened a fundraisers' steering group in November to iron out charities' problems with the scheme's contract.
The board began issuing a revised printed version last week. Other dropped clauses include a requirement for charities to include details of complaints about fundraising in annual reports and a requirement to provide the public with a designated complaints co-ordinator's contact details.
Consumer consultant Mick McAteer, a former principal policy adviser at Which? who commented on the FSB's initial consultation, said: "The decision to drop the requirement to summarise complaints information and how complaints are resolved undermines transparency and accountability."
Steering group member Giles Pegram, director of fundraising at the NSPCC, said: "There was detail that wasn't well-worded. It wasn't clear whether volunteers were part of the charity or were donors."