Four-letter route
Trace EXIT from row 2, column 3. Go up to row 1, column 3, then turn right through row 1, column 4 and row 1, column 5. The letters read E → X → I → T, so this route begins with the way-out clue and uses two straight segments.
For a cell-by-cell check, use: 1 at row 2, column 3; 2 at row 1, column 3; 3 at row 1, column 4; 4 at row 1, column 5. It rises once and then continues right twice, covering four cells with one turn.