I would like to try and edit the imported route on my laptop to represent the actual walk done by moving the marks along the straight line
It's probably a track
which you've imported. There are two possible methods:
Right-click on the track and use the Convert Track to Route option. You can then drag the waypoints and add any more that you wish (Right-clicks again). Then convert the Route back to a track (note that the intermediate tracks and routes are not deleted but only "hidden").
However, IMHO the better (but more tricky) method is to Split the track at the points where the "straight line" starts and ends, delete the line, create your own intermediate track and then join the tracks together again.
Both these methods have a few "gotchas", generally concerned with the "minimum update distance" set in the track properties. "Save As" the track before you start and ask again if you need more help.