intrude into something
to get involved in something that is someone else's business. I don't want to intrude into your affairs, but I see that you're short of money. Please don't intrude into this matter.
intrude oneself into something
to work oneself into some matter that is someone else's business. I hate to intrude myself into your conversation, but don't I know you? Please do not intrude yourself into this matter.
intrude (up)on someone or something
to encroach on someone or something or matters that concern only someone or something. (Upon is formal and less commonly used than on.) I didn't mean to intrude upon you. Please don't intrude on our meeting. Please wait outside.