Linking your Team library to a managed library on library.io is a one-way link. Your local library will receive updates from the managed library, but local updates cannot be pushed up to the managed library.
Your Team library can be linked to only one managed library at a time. If you want to link to another managed library, first unlink from the current one, then link to the new one.
If you want two-way update links between your Team library and a managed library, push your Team library to library.io to create a new managed library.