Her paternal aunt puts her money in a riba-based bank; can she accept her hospitality?

Firstly: 

If your aunt
has another, permissible source of income, such as a salary from permissible
employment, there is no sin on you if you eat her food and accept her
hospitality, because what the scholars have stated is that if a person’s
wealth is a mixture of halaal and haraam, and they cannot be told apart, it
is permissible to interact with him, buying and selling, lending and
borrowing, etc. It is also permissible to eat his food. The Prophet
(peace and blessings of Allaah be upon him) and his companions interacted
with the Jews, and they ate their food, although their wealth was not free
of haraam elements, because they took riba and consumed the people’s wealth
unlawfully. 

But some
scholars say that wealth which is acquired via riba is haraam only to the
one who acquires it, and there is no sin on the one who takes it from him in
a permissible manner, such as if it is given as a gift or offered in
hospitality. 

Shaykh Ibn
‘Uthaymeen (may Allaah have mercy on him) said: 

Some of the
scholars said: If something is haraam because of the manner in which it was
acquired, the sin is only on the one who acquired it, and not on the one who
takes it in a permissible manner from the one who acquired it, unlike that
which is haraam in and of itself, such as alcohol and goods confiscated by
force, etc. This is a strong argument, based on the evidence that the
Messenger (peace and blessings of Allaah be upon him) bought some food
for his family from a Jew, and he ate from the sheep that was given to him
by the Jewish woman in Khaybar, and he accepted the invitation of a Jew,
although it is known that most of the Jews deal in riba and consume haraam
wealth. End quote from al-Qawl al-Mufeed ‘ala Kitaab al-Tawheed
(3/112). 

He also
said: As for that which is haraam because of the way in which it is
acquired, such as that which is acquired by way of deceit, riba, lying, and
so on, it is haraam for the one who acquires it, but it is not haraam for
others, if they acquire it in a permissible way. This is indicated by the
fact that the Prophet (peace and blessings of Allaah be upon him) used
to interact with the Jews even though they used to consume haraam wealth and
take riba. That indicates that it is not haraam for anyone other than the
one who acquires it. End quote from Tafseer Soorat al-Baqarah
(1/198). 

But if your
refusal to accept this hospitality will affect your aunt and make her repent
from this haraam action, then undoubtedly it is more appropriate for you to
refuse this hospitality. 

And Allaah
knows best.