The phrase "not be any the wiser" is often used to indicate a lack of awareness or understanding about a certain situation or event. There are several synonyms that can be used to convey a similar meaning, including "clueless," "unaware," "ignorant," "oblivious," and "uninformed." Each of these words can be used to describe a situation where someone lacks knowledge or understanding about a particular topic. For example, if someone is clueless about current events, it means that they are unaware of what is happening. Similarly, if someone is ignorant about a particular subject, it means that they lack knowledge or understanding about it. Overall, these synonyms help to convey the idea of a lack of knowledge or awareness.