For some reason I can’t edit a curve once the brush has been placed / used. However when I click on the new geometry it changes. To narrow things down a bid, using a braid brush from BadKing, but the default strap does the same.
You can edit the default curvestrapsnap. Tried also braid brush from badking and it is also editable (brush version). Unless there is another braid brush that I don’t know. The rule is to touch the line once has been created and will be editable. If we touch the geometry of the mother object instead then the insert brush becomes fixed geometry and it is not editable by curves.