"Wreaking vengeance" generally implies seeking justice or revenge by causing harm or punishment to the perpetrator. Some synonyms for this phrase could be "inflicting retribution", "administering punishment", or "meting out revenge". Additionally, other phrases that convey a similar meaning include "getting even", "taking revenge", or "settling the score". While these phrases may have different connotations and nuances, they all convey a sense of seeking justice for a wrongdoing. Ultimately, the use of language is important in expressing the attitude and tone behind seeking vengeance or retribution, and it is crucial to choose words that accurately convey the intended message.