Stephen,
Try deleting the connection from CMC. If you have any rules / tasks bound to that connection sources, then you will not be able to delete the connection. You have to first delete the tasks / rules that were bound to that connection sources and then finally you can delete the connection,
If you successfully delete the connection from CMC, you won't see that database in Data Insight Connections tab of Metadata Management and also you will not be able to use that in your data insight project.
Hope the above information helps.
Thanks
Sreeram