What does Atticus think of Boo?
Always respectful of everyone, Atticus feels that Arthur Radley's privacy should not be invaded by the children, and he understands that Boo is a mockingbird, who should not be harmed by the curious and gossips and predatory types. Later on, he is also extremely grateful to Boo for having protected the children from Bob Ewell.
Early in the narrative when the children's curiosity moves them to invade the privacy of the Radley yard, Atticus scolds them after Jem tries to put a note on the window sill.
"Son,...I'm going to tell you something and tell you one time: stop tormenting that man. That goes for the other two of you."
Further, Atticus informs the children that what Mr. Radley did was his own business. He instructs them that the proper way to communicate with someone is to go to the front door, not to put a note on a window sill. Finally, he tells the children to stay away unless they are invited.
In the final chapters, after Boo Radley kills Bob Ewell in order to save Jem and Scout from his attack with a knife, Boo is brought into the Finch home. When Scout greets him, saying "Hey, Boo," she is corrected by her father to call him "Mr. Arthur." In addition, when Sheriff Tate makes his argument to say that Ewell fell on his knife rather than implicate Arthur Radley, Atticus agrees with Tate's words that
"...taking the one man who's done you and this town a great service an' draggin' him with his shy ways into the limelight--to me it's a sin."
Considering Tate's words, Atticus turns to Arthur, "Thank you for my children, Arthur." Clearly, then, Atticus has great respect for the privacy of Arthur Radley; moreover, he is extremely grateful to him for having protected the children from great harm.