K, as things currently stand we don't seem to be able to save or edit an imported route in the app. There is, however, an easy (and I think superior) alternative: 'upload' the route via the website, save it (or edit it) there and it will then be available on the app. Simply go to 'My Journeys', scroll down and tap 'upload'. Once the imported route is saved, it will be available in the app.

On a side note, I am not a fan of transferring routes between different platforms. Komoot, as just one example, makes different choices to CT. When you find yourself on a lethal road, hitting a dead end or looking for a road that does not exist that'll be Komoot's fault - not CT's :-)

HobbesOnTour, thank you for your comment. I also tried that: I uploaded routes to CT via its website. However, when I navigate them and do not stick to the route in order to spontaneously make a detour, take a shortcut or go further - which frequently happens to me - this "new" route cannot be recorded at the end of the journey. In other words, only the planned and imported track, which is already recorded before navigation, is kept in CT, not the route actually followed.
I also appreciate your other comment and agree that we should avoid transferring tracks from one platform to another. However, as it happens, before discovering CT I had already planned a number of trips on other sites and don't want to start from scratch.

However, when I navigate them and do not stick to the route in order to spontaneously make a detour, take a shortcut or go further - which frequently happens to me - this "new" route cannot be recorded at the end of the journey. In other words, only the planned and imported track, which is already recorded before navigation, is kept in CT, not the route actually followed.

K, that's because CT doesn't record the route.

However, the new 'Tiles' feature as highlighted in the Supporters' Newsletter might be of use:

Introducing Travel Tiles!

A brand new fun feature on cycle.travel’s app and website this month – Travel Tiles.

This is a grid of places you’ve ridden. The more places you ride, the more hexagons light up. It’s an enjoyable way to record places you’ve cycled and to give you ideas for new places to ride.

Whenever you ride anywhere using the cycle.travel app, the app takes a note of the hexagons you’ve ridden through. You can view them by choosing “Travel Tiles” from the map menu (top right).

The hexagons stay on your phone by default, but you can also choose to save them on the cycle.travel website. Use the “Upload Travel Tiles” option from the Settings menu for this. (You can set the app to automatically upload tiles whenever you finish a ride.)

Then on the cycle.travel website, you’ll be able to see your tiles at your user page (“My 🚲”). Or turn them on when using the route-planner, again with the map menu at the top right. You can then use the route-planner to plan routes that take in unvisited tiles.

In relation to:

I had already planned a number of trips on other sites and don't want to start from scratch.

Rather than import a gpx track into CT directly, we can import the gpx as a 'trace'. This is simply a line on the map - it is not a route. Then, we can plot a route choosing the same start and end points, add in any viapoints and compare the imported route to CT's one. It's not much work and gives peace of mind. You'll find 'trave gpx' at the bottom of the 'Hamburger menu' on the map page. 

Thank you for your valuable feedback, HobbesOnTour!