Any requirements conditional to the grant ought to be agreed in writing and once the project has got underway, you should keep the trust informed of progress and fulfil any special reporting requirements.
If your appeals are so successful that you have more money than you need for the project, then you must return the parts back to the trust, unless they give permission otherwise.
And if your appeal to a trust isn't successful, then you should accept the trust's decision.
In co-operation with Association of Charitable Foundations the Institute has produced the Fundraising from Grant Making Trusts Code of Practice (223kb).