How to remove black glue from Arches paper border?
You will have the same problem with watercolor-blocks that are glued on the edges, only that you see the remains of the glue better when the glue is black. What I usually do to remove the glue is one of the following.


Cut the edges with a sharp scalpel (or another sharp knive) preferably with the help of a metal ruler.
Lay the paper flat on a hard surface and scratch the edges (e.g. with your nails) until the glue is gone.


I dont think there is a non-invasive way to remove the glue, as it is made for holding the paper to the block really tight - even when wet.