A back-handed compliment is a statement that is seemingly positive but has an underlying insult or negativity. There are several synonyms that can be used in place of this term, such as "left-handed compliment," "insincere compliment," or "insulting compliment." Other options include "damning with faint praise," "grudging praise," or "veiled insult." These phrases all describe a comment that appears to be complimentary but actually contains an insult or condescending tone. It's important to recognize these types of back-handed compliments and understand their true intentions, as they can be harmful and disrespectful, even if they sound positive at first glance.