Is it permissible to take a transportation fee from the money designated for charity, which one is entrusted to distribute, without the knowledge of the owner of the money?

If you are asked for the costs of transferring funds for distribution, you are entitled to claim them. If the owner of the money permits you to take the costs from it, then there is no harm. However, deducting them without his knowledge is not permissible, due to the Prophet’s (peace be upon him) saying: “The wealth of a Muslim person is not permissible except with his willing consent.”

If the funds are Zakat (definition), then it is not permissible to deduct the wage from them, according to the more preponderant opinion, because that would diminish them from their rightful recipients. Consequently, you should take your wage from the owner of the Zakat.