To edit a box that is mapped from another guide, click on the "recycle" icon in the upper left-hand side of the box. This will reveal the guide from which the original box comes. Just go to the original guide to edit your content. (N.B.: if you are not an editor or owner of the original guide, you can either ask the guide owner to update the content or you can re-copy the box and select "make a copy" as you do so—this will allow you to edit the copied box.)
The same principle applies to mapped items. Select the "original guide" to edit an item, or you can do so from the Content > Assets menu in the main LibGuides toolbar.
Editing mapped pages is similar, but LibGuides will point you to the original guide directly.
