Rebbe Nachman teaches that there are 24 batei dinim that are rendering judgement upon the world. When a pidyon is given, a Tzaddik is able to sweeten all the judgments that come out from these batei dinim. However, sometimes, it may not be possible to sweeten these dinim (judgements). The key way all the dinim are sweetened is through bringing in geirim, which renders the one who is misgayer (converting) people to be in the aspect of Moshe Rabeinu, who changed people from Shmad (Baptism) to Ratzon (Delight). This is shown through the Gematrios of those words, Moshe being in the middle at 345, Shmad 344, and Ratzon 346. He teaches that through making geirim we nullify the power of avodah zarah (idol worship) throughout the world, which lessens Hashem’s anger with us.
From this we can see the preciousness of bringing in geirim. Though it does say in the gemoro in Kiddushin “Geirim koshin l’Yisroel k’sapachas,” (Converts are hard on Yisroel like a skin problem), we have to consider each of the approaches Tosfos and Rashi bring. One side is that converts revert often, rachmono litzlon, to their old ways; the second aspect is that they often don’t know how to learn and thus come to great errors; and the third is that the geirim do so well in learning and serving Hashem that they make all the other Yidden look bad.
So in relation to what Reb Nachman teaches here and in other places, along with general principles taught in sifrei Chassidus, we can see that bringing in geirim accomplishes a huge Tikkun. However, it cannot simply stop at the mikvah. To make sure a convert doesn’t switch back to their old ways, they must be not only accepted but also educated properly in the ways of Torah and Yiddishkait. By this, I do not mean simple indoctrination, but rather how to sit and pore over a masechta Gemoro and come to love the Torah and know Hashem through it. Though the work can be discouraging at first, as teaching anyone something new, one must keep to it and this is the true fulfillment of the mitzvos to love geirim, and effectively the elimination of Hashem’s anger upon the world caused by avodah zarah. When new people are brought to serving Hashem properly, with true love and devotion, especially through the d’veikus that is possible only through learning Torah, this certainly fulfills the Tikkun Reb Nachman speaks of in Likutei Moharan.