The expression "not give a tinkers damn" is a colloquialism that implies a lack of interest, concern, or respect about a particular subject. However, there are several other words and phrases that convey a similar sentiment, including "couldn't care less", "not bothered", "indifferent", "apathetic", "unconcerned", and "nonchalant". Each of these synonyms can be used interchangeably, depending on the context of the conversation or situation. Whether it's a casual conversation or a serious matter, there are plenty of ways to express disinterest or lack of concern without resorting to profanity.