Looks like a Joomla template menu assignment issue. Your forgot login page doesn't have a menu item assigned to it so Joomla is falling back to default template for its display. Typically your default template should be the template that allows component rendering while you assign the Home page to a separate template for example.
So your options are to fix your template assignment configuration (ideally the best option) or create a Joomla menu item to CBs forgot login page, which CB does create when it's first installed so was either deleted or unpublished.
N.B. Please note that we have a valid licence only for our production website which is...
We don't do licenses here. You can use CB and all our products on as many sites as you like.