If the Amerindians migrated from Asia, then it’s potentially plausible that remnants of their language(s) persisted through the decades. The Chinese greeting is “Ni hao” and could have lingered through migration as it was derived among the numerous tribes. Given that modern languages still have remanants of ancient Sanskrit, it’s possible that “how” or rather “hao” has done likewise.
Not to mention the fact that I’ve not seen any indication that proto-Amerind is related to proto-Chinese. Nor, to my knowledge, are the peoples in question ethnically related.
It is not even certain yet how North American (or South American) languages are related, beyond the fairly obvious families like Iroquoian.
While on this subject, one might add that specialized greeting words are relatively rare to begin with. As far as I know, no European language has a word that genuinely translates “Hello”, and “Hello” itself appears to have been coined by Thomas Edison as a better way to answer the telephone than Bell’s original “Ahoy!”. (“Hallo”, “Hillo”, “Hollo”, and “Hullo” are all much older than Edison, but they all mean things like, “Hey!”, “Look there!”, or “Gee!”) Most languages greet with phrases that actually mean something, such as “Good morning!” or “Peace!” Most languages also greet differently on the telephone than in real life. For example, one answers a telephone in Italian with “Pronto!”, which means “Ready!” If you use “Pronto!” as an in-person greeting, though, it means (depending on the circumstances) “Hello Sailor!” or “How much for doggy-style?” etc…