Gift Aid conundrum

I'd be grateful if a tax expert could answer the following question:

A person paying tax at higher rate makes a donation to a charity, and wishes in their tax return to claim back from HMRC the difference between the rate paid and basic rate on the donation.

Is it necessary for the charity actually to claim Gift Aid on this donation? The charity is quite small and doesn't want to bother with the additional administration which claiming Gift Aid would cause them.