The phrase "poke into" means to investigate or explore something in depth. There are several synonyms for this phrase, including delve into, probe, examine, scrutinize, and investigate. Delve into suggests a thorough exploration, while probe implies a more focused investigation. Examine and scrutinize both refer to a careful inspection of something, but examine can also suggest a more casual observation. Finally, investigate implies a more formal and systematic approach, often associated with legal or criminal proceedings. Regardless of which synonym you choose, they all suggest a deep exploration or inspection of something, with the goal of uncovering more information or understanding.