There can be no historic inverse of greet, if, as it seems to me, greet once meant both, just as much as good day, sir can be used for "good-bying".
dict.cc gives dismissal second to farewell as translation for Ger. Verabschiedung. I don't even know in which context they see it, but it already shows some negative connotation. We see Icelandic græta "to make (someone) cry, drive to tears" linked to greet, and the noun grata further as "mourn". The association may be passover, funeral, to condole, to pay respect? For grata we see PGem grētaną, "to weep, to cry" (from the PIE root *ǵʰreh₁d-, "to sound"), whence the verb *grōtijaną, "to cause to weep, make cry; to scold, to address (an issue), to address (an individual); greet", whence e.g. above* græta* and also our English greet.
We might see a remnant of this in German vergrätzen (synonym vergraulen, vergellen, verdrießen and more explicit verstoßen) "to alienate, to chagrin, to anger (as much as to make one leave)". I'm not sure, couldn't find anything specific in my usual sources.
Therefore, it depends on context, and the most general context is to holla.
You should also consider the many different languages parting greetings that amount to "see you soon/next time" and look for a word for this. I think it might be acceptable, if a bit archaic, to say
he parted with a greet
and along the lines of to bid ones farewell, to say
to greet ones parting
But of course that's not idiomatic, otherwise you wouldn't be asking.
We see the same in-and-out correspondence in military jargon
to salute, salutation
That would fit, but not in all contexts.