how to see miles remaining on a Inreach route

There wouldn't be a built-in way of doing that, other than using the scale information at the bottom left of the map to estimate the remaining distance. Another option would be to use an online calculator to measure the distance between the coordinates of his last tracking point and the coordinates of the end point of the route. In either case, this will be an "as the crow flies" distance rather than the actual remaining distance of the route.