Mourning, weeping, lamentation.
"The villagers gathered to greet the fallen hero's spirit with tears and sorrowful chants instead of cheers."
send greetings to
"She stopped by the front door just to greet her neighbors before heading out for a run."
To welcome in a friendly manner, either in person or through another means such as writing.
"When he saw his old friend from childhood, the man began to greet her with tears streaming down his face."
To weep; to cry.
Great.
"The server greeted us by name as soon as we walked through the door."