Thank you very much to both of you. Those pieces of code are much more than hints and are greatly appreciated.

The FrameTicks -> None option is definitely what I needed. I just wanted a box around the graphic. (For some reason I thought the Frame->True and Axes->False should do that but clearly it didn't.)

My real application does involve Manipulate in a CDF which is why I surrounded things with that command. I'm not at liberty to discuss the topic of the application but I can say that I have about 1,000 hexagons in a hexagon grid in which each hexagon is associated with different variables for which an analysis summary would be displayed. I wanted something to allow the user to select a point on the graphic in which I could then determine which hexagon was selected as I can determine the coordinates on the graphic for each hexagon and determine the hexagon with the closest hexagon center. (The hexagon grid on the graphic is likely not regular/uniform enough to allow me to apply the formula for hexagon grids to identify hexagon cells that I've forgotten so long ago.)

But first I needed to know how to capture the coordinates at a mouse click and the two of you have supplied ways to do that. Thanks!

I am not 100% sure I understand what you are wanting, but here is a stab at an answer anyway ;-)

First, your graphic doe not have axes, you have removed them, but you do have a frame. perhaps you are wanting the frame ticks to be removed and be left with only a plain rectangle. You can do this by adding the FrameTicks -> None option.

However, the following example I am doing things slightly differently. The Manipulate in your example is not at all necessary since nothing is being manipulated. So here is a bit of code that does what I think you want: that the coordinates do not appear unless you click on a point in graphic and that when you move your mouse without clicking the coordinates do not change.

DynamicModule[{position = None},
 Column[
  {
   EventHandler[
    Framed@ca, {"MouseClicked" :> (position = MousePosition["Graphics"])}],
   Dynamic[position]
   }]
 ]

Is this the sort of thing you are looking for?