The phrase "obtrude into" refers to the act of entering or intervening in a situation or conversation without being invited or needed. Some synonyms for this phrase are "intrude," "interfere," "butt in," "interject," or "impose." Each of these words reflects a different facet of the intrusive behavior that "obtrude into" describes. "Intrude" suggests a sense of violation or invading personal space, while "interfere" highlights the unwanted disruption caused by the action. "Butt in" is a colloquialism that emphasizes the abruptness and lack of consideration involved, while "interject" implies a sudden interruption of speech. Lastly, "impose" connotes a sense of burdening or forcing oneself onto others.