It's updated every week from OpenStreetMap. So if you make the changes on OpenStreetMap, cycle.travel will notice within the week. (Alternatively, if you like, you could post the changes here – perhaps saving a route to show the new NCN route? – and I can add it to OSM when I have a spare minute.)

In a spirit of adventure I had a go.

I think I managed to correct a section of NCN1 shown in error, and maybe a short stretch of NCN179 but I don't feel confident.

I've left a coupl of notes on OSM regarding renumbering of RCN18 as NCN179 and completion of Ranger signing on a stretch of NCN177.

I'll try about more correction on NCN17, maybe I'll get the hang of it soon.

It looks as if my first foray into OSM editing was an unmitigated disaster for other users.

I've apologised to the OSM member who put things back the way they were.

They've now let me know that it looks like Richard has straightened things out for me, so thanks a lot.  I've got a lot to learn before venturing onto OSM again.