One option would be to switch to a map that is centered on the Pacific ocean and splits the Atlantic. This might be the easiest to view.
Another option would be to examine the inter object (probably a list with x and y, but I am not familiar with the exact functions used) and see if the x coordinates tend to increase or decrease. Look for the place where they suddenly jump the other direction and insert an NA there (and in the same place in the y values), then the lines crossing the entire plot will not be shown. If that does not work you could insert an NA anywhere that the distance between points exceeds a threshold.
Another quick idea that may be good enough (partly depends on how many points are used for each curve) is to plot points instead of lines, use points(inter, pch='.')
instead of the lines command.