Is it appropriate for the family of the deceased to offer food or similar refreshments to those attending the funeral?

It is considered disliked (makruh) for the family of the deceased, who are already grieving and distressed, to prepare and serve food to guests coming for condolences, as this would cause them additional trouble and anxiety. (Ibn Abidin, Radd al-Muhtar, 2/240) Instead, it is Sunnah for neighbors or relatives to offer food to the family of the deceased and those who have come from afar. (Tirmidhi, Jana'iz, 21 [998])

There is no religious basis for the family of the deceased to distribute items such as halva or bread at the cemetery or at home. While it may be said that there is no harm in doing so as long as it is not considered a religious obligation, there is a danger that such practices may soon be perceived as a religious ruling related to funerals. Therefore, if these offerings are made as a religious requirement, they are considered bid‘ah (innovation) and superstition.

Source: T.C. Diyanet İşleri Başkanlığı, Din İşleri Yüksek Kurulu