Back in TS2009 3.1 days you could, but then after the 'upgrade' to build 3.2 you couldn't anymore and so it has been forever more. There's a very long queue of Trainz folk who have asked the same question you have asked and I doubt that anything will be done about it.
Display of spline points used to be toggled on/off by the keystroke combination Alt-O. Not sure if that still applies. In any case, look in Settings for a tickbox called Display Contextual Information (or something like that).
Under the menu in Trainz, there's an option to display contextual information, or something like that. Uncheck that box and that should hide the spline circles until you select that asset type, meaning select scenery splines and the spline points show up without spline circles on tracks. The same as with tracks, the splines disappear on the scenery items.
In the system menu of Trainz (not the Launcher) go to Settings -> Interface Settings -> Limit contextual information. Enable the setting to show only the spline circles of the active category (track or scenery spline). Disabling will always show the spline circles.
In the system menu of Trainz (not the Launcher) go to Settings -> Interface Settings -> Limit contextual information. Enable the setting to show only the spline circles of the active category (track or scenery spline). Disabling will always show the spline circles.
With a single mouse click, you can switch from the Splines tab to the Objects tab and the circles disappear. When doing any spline operation, you need to see the circles, otherwise you have no idea where the control points are. That’s why there is no option to disable them when you’re using the Splines tab.
