Does “under the impression” refer to “think"?
Great question! The word "impression" can mean a "thought", "idea", or "belief" about something. So the idiom "under the impression" can mean to "think" or have a "belief" about something. The only difference is that it also implies that the original thought or belief someone had was wrong. Ex: I was under the impression that he wanted to go to quit his job, but he actually loves his job.