There are several synonyms for the phrase "not let out peeping." Some of these synonyms include "keeping quiet," "maintaining silence," "keeping mum," "refraining from speaking," and "keeping a lid on it." These phrases all convey the idea of someone intentionally withholding information or not revealing something that they may know. It could be for various reasons, such as protecting someone's privacy, keeping a secret that has been entrusted to them, or simply not wanting to get involved in a particular situation. No matter the reason, these synonyms all describe the act of deliberately choosing not to speak up or reveal information.