Acerbic remark (4)
(Other definitions for barb that I've seen before include "Small prong on larger point" , "Twisted point of hook" , "Point of fish-hook - gibe" , "added to wire?" , "Jibe" .)
(Other definitions for put-down that I've seen before include "Crushing remark" , "Humiliating remark" , "Snub" .)