That is the wrong approach. Do not perform business logic (like updating UI controls) inside a drawing event.
In the OnMouse... event(s), take note of which column is being clicked on, and save that value somewhere, then invalidate the Grid to trigger a repaint before displaying the popup menu. When the popup menu is closed, clear the saved value and invalidate the grid again to trigger a new repaint. Then, inside the grid's OnDraw... event(s), check if the value is set, and if so then draw any cells belonging to that saved column as highlighted.