It is assumed that the paper strip is knotted into an open trefoil (forming a pentangle) that lies flat on the table, and that the two ends of the paper strip are continued up to spatial infinity. (See an image at http://upload.wikimedia.org/wikipedia/commons/4/4f/Overhand-folded-ribbon-pentagon.svg )
For a beginner in knot theory, the question has several issues:
1) Is the linking number defined for open ribbons? 2) Is it a topological invariant of open ribbons? 3) If so, is there an easy way to read it off the drawing? 4) Is the linking number the same as the (planar) writhe of one of the two edges of the paper strip?