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 you know for certain that these gifts which are offered to you by your neighbour (or his wife) are obtained through forbidden means, like bribery and the like, then in principle it is not permissible for you to accept them, as this is forbidden money which cannot be possessed by a person. It is obligatory to return the gifts which you took from them to their owners if they are known to you, otherwise you should not throw them, as throwing them is wasting money without a necessity.
Rather, you should get rid of these gifts by spending them on charitable fields; for more benefit on how to get rid of forbidden money and the religious requirements on this issue, please refer to Fatwa 83894. There is no difference between food and other items.
However, if you are not certain that these specific gifts are forbidden, and the person who gifted them to you has mixed money from lawful and forbidden sources, then it is permissible in this case to accept his gifts but it is more appropriate not to accept them as clarified in Fatwa 84314.
Since you do not know whether he obtained that money and food items from a lawful source or a forbidden source, then it is permissible for you to accept his gifts, as in principle a Muslim is free from any accusations (innocent until proven guilty).