A compliment with two meanings, one of which is unflattering to the receiver: “The senator said that her opponent was quite competent for someone so inexperienced; you hear nothing but left-handed compliments in these debates.”
Also, backhanded compliment. An insult in the guise of an expression of praise. For example, She said she liked my hair, but it turned out to be a left-handed compliment when she asked how long I'd been dyeing it. This expression uses left-handed in the sense of “questionable or doubtful,” a usage dating from about 1600.