The data presented is related to the paper An exploration of low crossing and chiral cosmetic bands with grid diagrams.
You can find below a spreadsheet containing the pairs of knots with fewer than 9 crossings, and with H(2)-distance one.
The first column gives the starting knot type, the second column is the knot type reached after a single non-coherent band attachment. The "grid" column gives a grid diagram representing the first knot, which becomes the second one after performing a non-coherent band attachment. The position of the band attachment, and whether it is performed on rows or columns, is specified by the "which" and "index" columns.