The phrase "poking into" implies intrusive or invasive behavior. Synonyms for "poking into" include prying, snooping, meddling, probing, intruding, and inquiring. Prying suggests a persistent and often unwelcome curiosity about someone else's business. Snooping implies stealthy or secretive observation of another's activities. Meddling refers to interfering or imposing oneself in another's affairs. Probing implies a thorough and investigative examination. Intruding suggests an unwanted intrusion into someone else's personal space. Inquiring suggests a more polite and respectful approach to obtaining information. All these synonyms convey the idea of poking into something that isn't one's own business. Using synonyms can give your writing variety and nuance.