My aunt works in a bank. Is it permissible to eat her food?

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, sallallaahu 'alyhi wa sallam, is His slave and Messenger.

It is your duty to exhort your aunt to leave working in the mentioned bank if the bank is one that deals in Ribaa (usury or interest). Working in such a bank is forbidden since the worker in that field either gets involved directly in Ribaa transactions or at least contributes to them. All these activities are forbidden in Islam. Jaabir reported that the Prophet Muhammad, sallallaahu ‘alayhi wa sallam, said: "May Allaah curse the one who consumes Ribaa, the one who gives it to others, the one who witnesses it and the one who writes it. All of them are equal in sin".  Also, Allaah Says (what means):  {Help one another in virtue, righteousness and piety; but do not help one another in sin and transgression. And fear Allaah. Indeed, Allaah is severe in punishment.} [Quran: 5:2]

You should make clear to her the dangers - in this life and in the Hereafter - of eating from Haraam (unlawful) earnings. This may prevent one’s supplications being answered by Allaah. If you believe that your not eating her food may have some influence on her to give up working in that bank, then you should not eat her food. Thus, your avoidance to eat her food would be considered an act to change the evil, which is a duty of all Muslims. If she does not care about your not eating her food and it will not influence her decision, then you may eat her food. Prophet Muhammad, sallallaahu ‘alayhi wa sallam, would accept gifts from Jews though their earnings were not good. The incident of him receiving the cooked poisoned sheep from a Jew is one such example from many. This story is narrated by Imam Al-Bukhari and others. Unless you are compelled, it is better for you to refrain from eating her food.

Allaah Knows best.