My assessment of this issue follows. Beware it is only informed by me looking at the extension components and it involves discussion of the internals of the module.
The extension adds a "Game Piece Layers" component to the module. This defines a layer property named "Layer" that it uses to order the display. Any piece that does not have this "Layer" property defined is normally displayed on top. The only pieces with this layer defined are the control and perimeter markers in the extension, so all other pieces are displayed on top unless the order is changed. The extension has 2 layer controls, the first button toggles the 'Control' and 'Perimeter' layers to be active or inactive (hides them). The second button adds a display layer control that cycles through the order in which the pieces are displayed, effectively cycling through "Control", "Perimeter", and "No value". Note that everything other than the extension provided counters has "No value" for its layer.
This VASSAL map component takes precedence over the VASL overlay display order in that the overlays use their own method (within VASL) to display on top of the map but under the other counters. They use the "Overlay" property (marking it 'true' if it is an overlay) so that the overlay is placed under the counters. Note that this VASL method does not create a new map layer within the main map component as far as VASSAL is concerned.
This conflict between the two display methods and ordering is what you see occurring when you use the extension. If you do not have the extension loaded, there is no "Game Piece Layers" component defined. If you have the extension, there is this additional component. Because all non-extension pieces are in the "No value" layer, the extension only has 3 defined layers it can manipulate, and both the overlays and the normal counters are in one layer. Within that one "No value" layer, VASL takes over and orders the overlays underneath the counters (at times) but occasionally it places them on top and you must SHIFT+Select the overlay and put it underneath the normal counters. This does not change the VASSAL display order, it only affects the "No value" layer. I do not see a function within the Layers control that allows you to always keep a specified layer on the bottom (i.e., overlays) so that it will not be manipulated. I suspect this is why VASL coded in their own Overlay property so that overlays would not get messed up. So technically the extension is the cause of some of these problems, however, it is the interaction between the VASSAL layers and the VASL overlays that is the real issue.
I have some initial thoughts on this and will be investigating more.
Bottom line is you can manipulate the control/perimeter counters by hitting the stacking order button and place them on top, allowing you to select them and move/delete at will. You can always hit the hide button to toggle their display at any time, which makes them unselectable as well. You will also always see them in the hover display if they are turned on, even if they are under the overlay.
I use this extension religiously for my campaign games. Control markers everywhere, perimeter markers everywhere. I always hide them when I am doing anything other than assessing my situation as far as control and what I am trying to do in the game. It is too easy to in advertently select a perimeter or control counter and move it by mistake.