Is there a ruling in Islaam that gives a person the right to claim back goods/money that was given out as present/gift after a fallout.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

It is not permissible to take back a gift, as the Prophet said: "A person who takes back a gift is like a dog eating what it vomited." [Al-Bukhari] The Prophet, also said: "A person should not take back a gift except a parent from his children, and the one who gives a gift and takes it back is like the one who vomits, then eats what he vomited." [An-Nasaa'ee]

Therefore, it is not permissible to take back a gift even if there is an argument or a dispute between the gift-giver and the person who received the gift.

Allaah knows best.