Enters their heads - Idioms by The Free Dictionary
enter (one's) head (redirected from enters their heads)
enter (one's) head
To be thought of by one. Take time to form your response to the interviewer—don't just blurt out the first thing that enters your head.
enter someone's head occur to someone (usually used in the negative).
enter somebody’s ˈhead be thought of by somebody; occur to somebody: It never even entered my head that we might not win.