The quote refers back to what Scout and Jem were told when they got air rifles for Christmas, not to shoot a mockingbird. A mockingbird doesn't do anything but sing many bird songs and harms no one. It isn't a predator or harmful to anyone. Tom Robinson and Boo Radley were symbolic of mockingbirds. Both men did nothing to harm anyone and were friendly to those in need. Boo was rumored to have stabbed his father in the leg with scissors in his younger years. Since then, he has done no harm, merely helped the children the night of the fire and given them little presents in the knothole. Tom was the only human being who was pleasant and helpful to Mayella Ewell. Their kindliness and helpfulness without expectations of return made them the mockingbirds of Maycomb.

Scout's observation at the end of the novel about protecting Boo Radley from suffering  shows how much she has grown up. Scout makes the connection between Boo and the mockingbirds Atticus had forbidden Jem to kill because she has come to understand the value of innocence and goodness and the evil of cruelty. This passage shows that Scout has adopted her father's values. It also serves to emphasize these major themes of the novel.

Arthur "Boo" Radley is a recluse in this story. He avoids people and does not socialize with the residents of the town. However, he is the real hero of the story. He is the guardian and protector of the Finch children.

Scout understands her father's admonishment about shooting mocking birds with the bb guns because mocking birds are not a pest, they just sing pretty songs and are a joy to have around.

Creating a fuss and having the newspaper interview Mr. Arthur Radley about his heroism would have brought an end to Mr. Radley's lifestyle. He would have been out in the public eye, and that would create even more problems for the Radleys.

So, bring Arthur Radley out in the public as a hero would have "outed" him without his consent.  Being a public figure would have "killed" his personality and his lifestyle.