Although I agree with you that their e-mail, text or whatever could have been phrased differently/better their premise is still valid. You and others were inadvertently awarded twice the amount they were expecting to award.
Integrity, definition: The quality of being honest and having strong moral principles; moral uprightness.
If you were to make a purchase for $35 at a store somewhere and paid with a $50 bill, then received $25 in change, would you point out the error and return the excess $10 or would you keep it?
This is where personal integrity comes into play.
One of the wisest human I've ever known once told me, "When you die the only thing you can take with you is your integrity."
You only get one chance to make the right decision in matters such as this. Make the right one you'll never regret it, make the wrong one you'll never forget it.
Do you really think you'll sleep better knowing you kept money intended for a charity?
Just give it back. You'll feel better about yourself. If you're still unsure, then ask yourself why did you started this thread. You probably already knew what the right thing to do was in the first place.