I'm not a regular user of iD, but it looks like what you'd need to do is:
Split Thorndale Lane where the path to the east joins, and remove the northern bit from the Chalklands Way relation (at the bottom of "edit feature" in iD there's a "relations" section).
Then add the path to the right to the relation.
The next bit is to try and edit other ways that should / should not be in the relation as well.  The current route is https://www.openstreetmap.org/relation/8163036#map=14/54.0180/-0.5875 , so presumably that bit of A166 shouldn't be in it, and part of Southfield Road should, be, and enough to join with the section that heads northwest.
It'd be good to record where the route markers are for it as well - they show as circles on https://www.openstreetmap.org/relation/8163036#map=14/54.0180/-0.5875 , but as you'll have seen the Chalkland Way ones are small, hard to spot and often seem to be missing.