Breakpoint function: Removing or replacing points

Hi
I have been struggling to figure out if there is a way to remove or replace the points on the breakpoint functions
I do not want the user to have the ability to add a point on the same index on the x axis as another point, it would be better if I could replace or delete the point that is on the same index.
Is there a simple property of the object I could change or something I could add in the way of checking the points and removing them

Thanks in advance, this is my first post to any forum ever so apologies if I have put this in a wrong category or done something wrong etc

James