The phrase "poke one's face in" implies a sense of intrusion, meddling, or unwanted involvement in someone else's affairs. There exist several synonyms for this phrase, including "butt in," "interfere," "meddle," and "nose around." Each of these words suggests a degree of overstepping boundaries or sticking one's nose where it doesn't belong. Other similar phrases include "prying into," "interjecting," "sticking one's oar in," and "sticking one's nose in." Regardless of the specific phrase used, they all convey a sense of unwanted interference that can be frustrating and irritating for the person on the receiving end.