To start, let's break down the phrase. "Iribitari" can be translated to "invitation" or "request," "Gal" refers to a type of Japanese slang for a girl or a young woman, "Manko" is a rather crude term for female genitalia, and "Tsukawasete Morau" is a polite way of saying "to receive" or "to get." "Hanashi" translates to "story" or "talk."