Did Jem and Scout ever write a note to Boo?

Yes, Jem and Scout do write a note to Boo Radley. In chapter 7, they decide to thank Boo for the gifts in the knothole,

"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.