Looking at 15.2 there is no secure option for task edit properties sub pages.
I created a Subpage for the task edit properties page and a section in it.
There is the display condition option
That allows you to restrict the access to eg members of a group.
My understanding it that when you have an attribute on subpage with a display condition and you have it elsewhere eg. in the task list you can see it there. If an attribute is on a secured subpage its values are plank elsewhere where it occurs.