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.
If this money was given to you by a non-Muslim as a gift then there is no harm to accept it on the condition that this does not entail having any affection towards him, supporting him and being an ally to him, or that it involves renouncing some religious rulings. For more benefit, please refer to Fatwa: 88293 regarding the limits of a relationship between a Muslim and a non-Muslim. So in case it is permissible for you to accept this gift, it is permissible for you as well to dispose of it as you please in all permissible ways including spending it for the purpose of going to 'Umrah.
However, if this money which the non-Muslim has given to you, was given to you as a trust or a deposit to keep for him, then it is not permissible for you to go for 'Umrah with it or to spend it as you wish except with his permission.
Allaah Knows best.