Alexei Kassian made a Swadesh list of Hurrian language and compared it to reconstructed proto NEC language and it turns out that there is not much good cognates between this two languages. Based on this he dismissed the possibility that NEC and Hurro-Urartian are genetically related.
Swadesh list of 100 words is believed to be the most stable part of basic vocabulary of any language and the presence of cognates in this list is very important.
After this he compares Hurrian with distinct branches of NEC and finds three good cognates of proto-Nakh and Hurrian. The remarkable thing is that those three words are absent in other NEC languages and are quite specific to Nakh. According to him Nakh languages (Chechen, Ingush, Batsbi) separated from each other circa 2-nd century BC, while proto Nakh is usually believed to have separated from other NEC languages at 2800 bc.
He concluded that those three words of basic vocabulary might be lownwords from Hurrian.
Now when we look the Y DNA of Nakh people we see that it confirms the recent dispersal of this branches. We also notice that Nakh people had some unusual DNA that is absent or rare in other Daghestani people. Based on this we can imagine that some of the founding fathers of Nakh people had non-NEC origin. If further research shows that Nakh languages do have extra Armenian or Iranian words that are absent in other Daghestani languages ( an idea that is plausible if Mudrak is correct ) then we can imagine that those young lineages had introduced those Hurrian, Armenian and Iranian terms in the region were proto-Nakh population was dwelling. At last now thanks to ancient DNA we know that Q found among Chechen people (https://www.yfull.com/tree/Q-YP4055/) had Alanian origin which ironically was lost in Ossetians.
Kassian also made a list of Hurrian and Urartian cognates.
Links in the comments.