Because Walter had to sacrifice himself by traveling to the future to reset the timeline, he is erased from 2015. The paper serves as a wordless goodbye, signaling to Peter that Walter succeeded and is at peace. 📼 Other Important "Papers" in Season 5

The "paper" you are referring to is the drawing that appears in the final scene of the series finale, "An Enemy of Fate". 🌷 The Meaning of the Paper

Early in the season, Walter finds a large sheet of paper filled with equations—the original plans for the machine to defeat the Observers—hidden in his lab.

At the end of Season 5, after time is reset to 2015 and the Observer invasion is prevented, Peter finds an envelope in his mail from Walter.

While not paper, the team follows a series of Beta tapes hidden in amber by Walter to reconstruct the plan step-by-step. FRINGE Recap: 'The Recordist' - Give Me My Remote