Jem and Scout do write their mysterious neighbor, Boo Radley, a note in Chapter 7 of Harper Lee's novel, To Kill a Mockingbird, but, sadly, it never gets into his hands. Jem and Scout had already received some gifts from the knothole in the tree on the corner of the Radley lot--gum, a knife, carved figurines and a coin. After ruling out the possibility that they could have come from Miss Maudie--
"Ar-r, Miss Maudie can't chew gum... (it) cleaved to her palate and rendered her speechless," said Jem carefully.
they decided to thank Boo.
"Dear sir," said Jem. "We appreciate the--no, we appreciate everything which you have put into the tree for us. Yours very truly, Jeremy Atticus Finch."
"He won't know who you are if you sign it like that, Jem."
Jem erased his name and wrote, "Jem Finch." I signed, "Jean Louise Finch (Scout)" beneath it. Jem put the note in an envelope.
However, we never find out if the note is delivered to the tree or not. The next morning on the way to school, Jem turns white and calls to Scout: The knothole has been filled with cement. Scout (nor Harper Lee) never specifically say if the note has been delivered to the knothole, but we can assume it has NOT; since the Finch children wrote the letter at night, they probably planned to place it in the tree the next morning on the way to school in the hope of finding an answer on the way back from school later that afternoon.
When Jem asked Mr. Radley why he had cemented the knothole, he responded that it was a normal way to handle a dying tree. But Atticus later told Jem the tree looked perfectly healthy. Jem then realized that Mr. Radley had deliberately found a way to restrain his brother's activities and that their contact with Boo had probably come to an end.
The children leave this note for Boo thanking and appreciating him for what they have done for him and they want to leave this for him. However, as they approach the tree where Boo has left all of his gifts, the kids find out it is filled with cement. When Jem asks Nathan Radley about why it is filled, he responds by saying the tree is dying, however when he asks Atticus, he responds that it was perfectly healthy. Jem feels extremely sad because he wanted to respond. This happened in Chapter 7