I was utterly amazed because the room was horribly dirty.
This is a combination of the word 呆れる meaning "to be amazed" and 返る meaning "to be returned." You're so amazed at something that it keeps returning to your mind. It means to be utterly amazed!
This is a combination of the words 呆れる and 返る. 呆れる becomes 呆れ and you just add 返る to it. So reading this should be pretty simple.