An embedded map on a website is embedded as “read only.” That means, the website visitors will not be able to edit the maps. The map visualizations do not show the “edit” link so visitors have no option to edit the maps.
You may embed your map on your website and notice that the Edit link is still visible. This is because you are still logged in to Mapline. Just log out of Mapline and go back to your website with the embedded map. Then you can see what your map will look like to your site visitors.