They will probably send the donated Bitcoin to the proper authorities. If they believed the same is really obtained illegally, it is absurd to give them back to the criminals. However, I doubt the stolen Bitcoin would still end up to their rightful owners even if it is turned over to the police. The amount is but a very tiny portion of what was probably stolen.

Personally, I would think it is better for this tiny amount to just serve a better purpose such as charitable works. But, of course, huge charitable institutions such as Children International wouldn't risk their reputation over 0.88BTC.