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.
First of all, please accept our condolences on the death of your grandmother.
Your cousin should be advised to stop raising this issue because on one hand he is not sure that what he said had really taken place, as he should have made sure about it because Allaah Says (what means): {O you who have believed if there comes to you a disobedient one with information, investigate, lest you harm a people out of ignorance and become, over what you have done, regretful.}[Quran 49:6]
Even if we presume that what he mentioned had really happened, this does not mean that he would blame you about this matter over which you have no control. In addition to this, the family of the dead is generally too preoccupied by the dead to welcome every comer. Rather, they deserve to be condoled and helped. The Prophet said (when the news of the death of Ja’far ibn Abi Taalib came to him): "Prepare food for the family of Ja’far as something has occurred to them that is preoccupying them.”
Furthermore, your cousin is a non-Mahram to you so it is not permissible for him to talk to you except when necessary and according to the necessity only.
Besides, it is not permissible to gather at the home of the family of the dead after the funeral as the Salaf (righteous predecessors) disliked gathering after the funeral and cooking food as they considered this as lamentation (which is forbidden) and we clarified this in Fatwa 133625. Also, it is not permissible to gather to supplicate for the dead; whoever wants to supplicate for him may do so wherever he is.
Moreover, it is not permissible to say that backbiting is permissible; rather, it is forbidden and it is one of the grave major sins. However, some scholars stated that sometimes it might be permissible for a preponderant benefit, and they gave some examples that we mentioned in Fatwa 81748.
Allaah Knows best.