FOX, the letter that Lee and Casey were talking about, one copy of the letter would go to authorities and the other would go to her Attorney. Based on that conversation of "trust", she wants to make sure what goes to the authorities is the same as to her attorney. People in jail are only allowed to write in pencil.
I am not sure why Casey said "rec" time as in recreational time. This might be to make Lee feel sorry for her as he doesn't have a clue what happens inside a jail. Most of their time is sitting in their cell, or within a certain area.
I highly suggest FOX call the jail and find out the daily schedule of an inmate rather than speculating on what "rec" means.