The phrase "gnaw away at" refers to the act of persistently and relentlessly consuming or eroding something gradually. Synonyms for this phrase could include words like corrode, wear down, eat away, nibble, chew, erode, scrape away, and consume. These words imply a gradual deterioration that can cause damage over time. The phrase may also convey a sense of anxiety or frustration that a problem or issue is constantly eating away at someone. It's important to have a diverse pool of vocabulary when communicating and writing, and utilizing synonyms can add variety and nuance to language.