Thanks Bill. I discovered that 'delete' will remove a selected chart object. It would be more intuitive if 'Remove Indicator' worked for objects as well.
Moving the Y-axis doesn't do the job. If you have a horizontal line that moves off the screen vertically, it is gone forever except that the text remains. But there is nothing that can be selected. Well, not entirely. All lines stop extending the right, so if you scroll back on the x-axsis the (static) lines are there. This includes the lines that never were off the chart; all extending stops when any one line moves off the chart (although I have one case that seems to be an exception; one line is extending the other is not).
It surely would be nice if objects persisted on charts. I've marked some charts where I have bought or sold with horizontal lines. But they will all be gone when I restart tomorrow.
See also Yahoo group about applying RE.