Can he take back the zakaah of his wealth if he gave it to a poor person then found out that he did not need it?

Firstly:

It is permissible to give zakaah to a sick person to spend on his medical treatment, if he cannot afford that. Please see the answer to question no. 105328 .

Secondly:

If someone gives his zakaah to someone who he thinks is poor or in need, then he finds out that he is well-off or is not in need, or that the poor person was able to save something of that (zakaah) money, then the giver has done his duty and he has no right to take back his zakaah.

It says in Zaad al-Mustaqni‘: If he gives it to someone who he thinks is not entitled to it, then it turns out that he is entitled to it, it is not regarded as zakaah except in the case of his giving it to a well-off person, thinking that he is poor. In that case it is acceptable (as zakaah).

For example, a man came asking for help and he appeared to be poor, so I gave him some zakaah. Then someone else came to me and said: What did you give him? I said: Zakaah. He said: This person is better off than you. In this case it is still valid, because we judge on the basis of what appears to be the case. An example of that is those who ask for help in schools and mosques, then we give to them on the basis of how they appear to be.

The evidence for that is the story of the man who gave charity one night. He went out with his charity and gave it to someone, and in the morning the people started saying: Last night charity was given to a rich man. He said: Praise be to Allah for a rich man, thinking that it was a serious mistake. Then he went out again and gave charity to a prostitute, and in the morning the people started saying: Last night charity was given to a prostitute. He said: for a rich man and a prostitute. Then he went out a third time and gave charity that ended up in the hands of a thief, and in the morning the people started saying: Last night charity was given to a thief. He said: Praise be to Allah for a rich man, a prostitute and a thief. It was said to him: As for your charity, it has been accepted. As for the rich man, perhaps it will be a reminder to him and he will give in charity. As for the prostitute, perhaps she will no longer need money and so she will refrain from adultery. As for the thief, perhaps  because what you gave him will suffice him and he will refrain from stealing. So his actions became useful and acceptable to Allah, and beneficial to those to whom he gave charity. From this it may be understood that if someone gives charity to a poor person and he turns out to be well-off, then it is still acceptable.

Some of the scholars are of the view that if he gives it to someone who he thinks is entitled to it after examining his case, then it turns out that he is not entitled to zakaah, it is still valid, even if he is not well-off. In other words, that applies in all cases, because the giver feared Allah as much as he could and tried his hardest to find out about the recipient of his charity, and Allah, may He be exalted, says (interpretation of the meaning): “Allah does not charge a soul except [with that within] its capacity” [al-Baqarah 2:286].

What matters with regard to acts of worship is what the accountable person thinks is the case. This is in contrast to interactions with other people, where what matters is what really is the case. It is difficult for us to tell him that his zakaah is not acceptable, even though he tried his best to find out what the situation was, and the one who makes the effort to find out will receive one reward even if he is mistaken; if he gets it right then he receives a double reward.

This view is more likely to be correct: if he gave it to one who he thought was entitled to receive it after studying his case, then it turned out that he was not entitled, his zakaah is still valid, because as it is proven that it is valid if he gives it to a well-off person thinking that he is poor, then the same applies in the case of other categories.

End quote from ash-Sharh al-Mumti‘ (6/264).

Thus we may conclude that your zakaah was valid, praise be to Allah, and you do not have to ask for any of it to be returned.

Thirdly:

It is not right for the one who is in need or the one who is taking care of him to take more than he needs, when he knows that it is zakaah money, and he should not accept (anything surplus to his needs), because of the general meaning of the words of the Prophet (blessings and peace of Allah be upon him) concerning zakaah: “The one who is well-off and the one who is strong and able to earn a living has no share of it.” Narrated by Abu Dawood (1391) and an-Nasaa’i (2551). Classed as saheeh by al-Albaani in Saheeh Sunan Abi Dawood.

The words “Zakaah is not permissible for a rich person, or for one who is strong and healthy” were narrated by Abu Dawood (1392), at-Tirmidhi (589), an-Nasaa’i (2550) and Ibn Maajah (1829); classed as saheeh by al-Albaani in Saheeh Sunan an-Nasaa’i.

Its says in Mataalib Ooli an-Nuha (2/259): If zakaah is given to someone who is not entitled to it because the giver was unaware of his situation, then the one who took it must give it back. End quote.

The scholars of the Standing Committee were asked: A widow is asking: I still have some of the charity money that was given to me, and also some zakaah money. One full year has now passed (since it was given to me); do I have to pay zakaah on it, and if I have to pay zakaah on it, how should I do so?

They replied: It is not permissible for this woman to take zakaah more than she needs. With regard to the money that she has, if it reaches the minimum threshold and one full year has passed, then she must give zakaah on it, at the rate of one quarter of one tenth, which is equivalent to 2.5%.

End quote from Fataawa al-Lajnah ad-Daa’imah, vol. 2 (8/381).

As your paternal aunt has died, and this money is left in the possession of her daughters, if they knew that their mother was not entitled to zakaah, or she took more than she needed, knowing that the money was zakaah money, then to be on the safe side it is more prudent for them to dispose of this money by giving it to the poor and needy.

If they included it in the estate and divided it, then there is no blame on them. Because the money was unlawful due to the manner in which it was acquired, it was unlawful only for the one who acquired it, and it may be inherited from that person when he died, according to the more correct scholarly view.

If the mother was not aware that it was zakaah money, or she was aware of that but she took only as much as she needed, or what she thought she needed, then some of it was left over, then there is no sin on her, and what she left behind is for her heirs.

And Allah knows best.