When someone is shedding "insincere tears," it suggests that their display of emotion is not genuine. There are several synonyms that can be used to describe this type of behavior. "Crocodile tears" is perhaps the most well-known term, referring to tears that are shed in a fake or insincere manner. "False tears," "fake tears," and "pretend tears" are other commonly used phrases. Additionally, if someone is described as being "tearful but insincere," it means that their display of emotion is not genuine. Using any of these synonyms can help convey a message of untruthfulness or dishonesty in one's emotional expression.