Praise be to Allah.
I.
Zakah must be given in full to one of the eight categories whom Allah, may He be Glorified and Exalted, mentions in the verse:
{Zakat [alms] is only for the poor and those in need; those who work to collect it; those whose hearts are to be won over; for the freeing of slaves; for debtors; for the cause of Allah; and for stranded wayfarers. [Thus it is] ordained by Allah, and Allah is All-Knowing, Most Wise} [At-Tawbah 9:60].
It is not permissible for the giver to ask for any of his zakah to be given back to him, because the condition is that ownership should be transferred properly to the recipients. Therefore, he should not take back any of it, whether that is by means of a stipulated condition or a trick or any other means.
Ibn Qudamah (may Allah have mercy on him) said: It is not permissible for any of it to be given back to the giver who was obliged to give it, because zakah is due to Allah, may He be Exalted, so it is not permissible for him to spend it in his own interests.
End quote from Al-Mughni, 4/106.
II.
If what came back to you from the state is a kind of deduction from the taxes that you owe because you gave your zakah or charity to some charitable organisations, then the money that comes back to you is yours; it does not affect your zakah and it is not like taking back some of the zakah or charity, because it is coming from a different source. So the money that is returned to you is not from the same amount that you paid, because the zakah that you gave will be given in full to those who are entitled to it, without anything being deducted from it.
This is a common practise in some Western countries which comes under the heading of social contribution, and in some Muslim countries under the heading of tax reduction commensurate with zakah given.
Among the recommendations of the Third Global Conference on Zakah in Malaysia was the following:
The Conferences applauds the practical steps that have been taken in some Muslim countries to adopt the principle of tax reductions commensurate with zakah given, and urges other countries to take the necessary legal steps to deduct from taxes the amount of zakah that was given. See: Masa’il az-Zakah al-Mu`asirah by Dr. Hasan al-Husayni, p. 537.
Based on that, if you paid $100 as zakah to the charitable organisations, then the state gave back to you $75 from what you had paid of taxes, or deducted that from what you owe of taxes, it is permissible for you to take what they give back, and you can keep what they waived, and that does not affect your zakah or detract from it.
For more information, please see question no. 146237.
And Allah knows best.
