It's a byproduct of temporality. You cannot create a new route of an existing timeslice. Looks like you still intent to have a gap when all is said and done is that correct?
I don't like gaps as they do nothing but cause problems but yet they are valid to have. We try not to create and then not mess with if we have to. We use Euclidean Distance for our gap calibration. Your measure may act differently depending on the setting and how you model your lrs.
One method I did today on 10.8 that looks good measure wise to completely fill in the gap that I could quickly see was to reassign the blue route with a later date then purple and blue to the purple route. Selecting the first gap segment as my target route. The measures populated matched the first gap segment.
Personally I probably would have created a new route with the correct date along the gapped section to be filled and second gap segment. I would then have retired the second gap segment from the start of the gap section and then reassigned the new route to the existing route with the same from date.
The image has the top half with the method I first tried and the bottom half shows the second method. Hopefully this all makes sense.