Is it necessary to re-issue the Zakat that was given to the grandmother, knowing that she did not accept it and gave it to the aunt?

It is not permissible to give Zakat to the grandmother because her maintenance is obligatory upon the son if she is poor, and this is the view of most scholars. Whatever was given to the grandmother from Zakat remains your responsibility, and it can be reclaimed and given to its rightful recipient, or an equivalent amount can be given out. There is no objection to giving the mentioned amount to the paternal aunt if she is among the eligible recipients of Zakat, for her to spend on herself or her dependents, and not for the grandmother's maintenance.