I recommend you not to put too much thought into this. According to your logic millions of Muslims would have a serious issue, which is simply not reasonable. And Islam is supposed to be reasonable.
It is true that interests are strongly prohibited in Islam..., surah 2, verse 275:
الَّذِينَ يَأْكُلُونَ الرِّبَا لَا يَقُومُونَ إِلَّا كَمَا يَقُومُ
الَّذِي يَتَخَبَّطُهُ الشَّيْطَانُ مِنَ الْمَسِّ ۚ ذَٰلِكَ بِأَنَّهُمْ
قَالُوا إِنَّمَا الْبَيْعُ مِثْلُ الرِّبَا ۗ وَأَحَلَّ اللَّـهُ
الْبَيْعَ وَحَرَّمَ الرِّبَا ۚ فَمَن جَاءَهُ مَوْعِظَةٌ مِّن رَّبِّهِ
فَانتَهَىٰ فَلَهُ مَا سَلَفَ وَأَمْرُهُ إِلَى اللَّـهِ ۖ وَمَنْ عَادَ
فَأُولَـٰئِكَ أَصْحَابُ النَّارِ ۖ هُمْ فِيهَا خَالِدُونَ
Those who consume interest cannot stand [on the Day of Resurrection]
except as one stands who is being beaten by Satan into insanity. That
is because they say, "Trade is [just] like interest." But Allah has
permitted trade and has forbidden interest. So whoever has received an
admonition from his Lord and desists may have what is past, and his
affair rests with Allah. But whoever returns to [dealing in interest
or usury] - those are the companions of the Fire; they will abide
And further, surah 2, verse 278/279:
يَا أَيُّهَا الَّذِينَ آمَنُوا اتَّقُوا اللَّـهَ وَذَرُوا مَا بَقِيَ
مِنَ الرِّبَا إِن كُنتُم مُّؤْمِنِينَ ﴿٢٧٨﴾ فَإِن لَّمْ تَفْعَلُوا
فَأْذَنُوا بِحَرْبٍ مِّنَ اللَّـهِ وَرَسُولِهِ ۖ وَإِن تُبْتُمْ
فَلَكُمْ رُءُوسُ أَمْوَالِكُمْ لَا تَظْلِمُونَ وَلَا تُظْلَمُونَ
O you who have believed, fear Allah and give up what remains [due to
you] of interest, if you should be believers. (279) And if you do not,
then be informed of a war [against you] from Allah and His Messenger.
But if you repent, you may have your principal - [thus] you do no
wrong, nor are you wronged.
And there are other verses I don't list here, but I hope that we understand that interest are considered very bad.
... but Islam is also the balanced way, the middle way, the way of mercy.
I don't have sources at the moment in this regard, but in this case maybe we try to reason.
You are making an assumption about the people. Even if you feel sure that they take interest, since you have no proof and no idea about the household's cash flow, it is not OK to assume they eat interests.
- You are supposed to assume the good, not the bad, from the people. As
far as I can understand, they seem kind people. Taking interests does not make them bad people per se.
- Also it is not OK to research with the goal to uncover a sin. If you
don't really know, then let it be. It is not recommended, sometimes
considered a sin, to try to prove someone's sins. When you witness,
then you are a witness and act with duties and rights of a witness, but don't try to find the bad.
- You, yourself, should try to not give interest and not to take interest. That is your part in society for a better and fairer economy. This concerns you, not the others. And this is the best part you can play really, because...
..., and this is the difficult part, the world is full of interest today. You cannot escape unfortunately. It starts already with the interest you take from your bank. You probably have no choice, if there is no Islamic bank in your area. You consume products. All global companies, even if not banks, are involved in interest economy. The company you are working for yourself, might be involved in interest economy.
I hope you see, that, although your intention is not bad, you risk to exaggerate. And exaggeration is not the middle way.
If it makes you feel bad, kindly refuse to join. Don't hurt the feelings. And leave a wonderful impression, so that this can be considered da'wa to Islam.
If it is a merely analytical question you were asking, then I am not qualified to answer this :-(
But ask God for forgiveness, whenever you can. And pay the zakat as good as you can, as this is considered to purify your fortune from the bad (which amongst others includes interest).