After a few weeks of posting insights from R' Shteinman on the parsha on Fridays I apologize for missing. One quick point:
The Torah tells us that Ya'akov refused to be comforted, to receive nechama, when he heard of the loss of Yosef. R' Chaim Brisker held that it is not only a mitzvah on the menachamim to console the mourner, but there is a mitzvah for the mourner to receive the consolation. R' Shteinman cites the gemara in Brachos which tells us that Rabban Gamliel was "mekabeil tanchumin" after his educated slave Tevi died; we see from here as well that consolation must be received. The Mesorah journal (Adar 5751, available here) quotes this same chiddush with what I think are two added points. 1) R' Soloveitchik held that this halacha of kabbalas tanchumin is part of the practices of mourning, nihugei aveilus. This is why mourning on the last day of shiva, where only part of the day is observed in aveilus, technically ends when the menachamim depart. What do the presence of menachamim have to do with whether the mourner is still obligated in aveilus? Because their very presence and the reception of their nechama demonstrates that aveilus is still being observed. 2) R' Soloveithik suggested that the mourner must actively acknowledge the nechama, e.g. nod his head, and not simply remain passive. This chiddush is based on a Midrash which says that Hashem continued to console the Jewish people after the churban habayis until they acknowledged his consolation.
It's not germane to this point, but an interesting chiddush in the journal article worth noting: the common practice is to address all the mourners as a group and wish them nechama. R' Soloveitchik suggested that this poses a problem of doing mitzvos chavilos chavilos and it is better to address each aveil seperately.