Is it permissible to go for Umrah or Hajj with money gifted by relatives?

It is permissible to perform Hajj and Umrah with gifted lawful money, and it is not required for it to be from one's original funds. One will receive a reward for it. Accepting a gift is permissible if it is given without solicitation or anticipation. It was narrated that the Prophet (peace be upon him) said to Umar ibn al-Khattab (may Allah be pleased with him): "Whatever comes to you of this money, while you are neither looking forward to it nor asking for it, then take it. And what does not, then do not crave for it." It was also narrated: "Whoever receives a favor from his brother without looking forward to it or asking for it, let him accept it and not refuse it, for it is sustenance that Allah has brought to him."

There is no objection to asking a grandmother for money for Hajj or Umrah with her, especially if the person asking for the money is in need and the grandmother would benefit from his accompanying her on the journey, because a grandmother is in the position of a mother. Providing assistance to her in her Hajj is considered an act of righteousness and maintaining kinship ties.