Mekubal's translation/analysis of Rav Eliashiv's teshuva (3:140)cited below by Rav Reuven Feinstein
Roni,
First a translation italics are my own comments in the translation:
From all of this it seems obviously we are missing parts already please provide those Roni that a mixed marriage, by means of this the non-Jewish spouse takes part literally they join themselves to or with in shiurim there is a good probability that it will enter into their hear to convert, and by means of this it causes the Jewish man or woman to be saved to return in repentance, there is to see in this b'diavad circumstance that there is to take hold of the understanding that it is permitted to teach Torah to a Goy if his mind is to convert. But in a situation that that this reason is not relevant, there is no place for a heter, this is Ossur.
Let us enumerate the conditions of the above heter:
1) Intermarriage 2) The Non-Jew seeks out and joins shiurim 3) It is permitted to allow them to take part b'diavad 4) Since there is a heter to teach torah to a non-Jew who is converting we can extend that to this case.
To be clear, R' Eliashiv makes a chumra(that one should not teach a person in the the process of Geirut Torah), as this opposes what is written in the Sh"A, but that is OK one can be Chumradik.
Then he removes his own Chumra in the case of an intermarried couple. If the non-Jewish spouse seeks out Jewish learning. His reason for this is that they may be convinced to convert, and thus in a round about way cause the Teshuva of their Jewish spouse.
What this leaves out is any mention of encouraging. Nowhere does R' Elishiv say לאמץ להתגייר he simply says that by them deciding to take part in Jewish learning there is a good chance that they will decide to convert, and we should not stop them.
To sum up. You brought an incomplete Teshuva, and presumably only the part that you thought supported your opinion. Examination of the language and grammar shows that this clearly does not support your position of actively seeking out or encouraging conversion. This is a heter to allow non-Jews in intermarriages who wander into shiurim, to sit those shiurim, that's all.
Rav Eliashiv's view on kiruv to intermarried couples as reported by Rav Efrati

==================================
Rav Reuven Feinstein
