The Theme is now only used to populate the style originally, and is not used after it is applied. Instead of the theme, you will generally want to interact through the tabbedView.style itself.
However in this case, the shadow is part of bar image itself. If you copy the "bar.png" and "email@example.com" from within the ShinobiEssentials.bundle, and modify them to remove the shadow, you can use your new custom image by creating an SEssentialsTabbedViewCustomImagesWrapper, assigning your new image to the wrapper.tabBackgroundImage, then creating your tab style as
[[SEssentialsTabbedViewStyle alloc] initWithTheme:[SEssentialsiOS7Theme new] customImages:wrapper];
This will remove the shadow from your Tabs.
We have now filed a task in our issue tracker to make sure this shadow is removed in future from the iOS7 themes.