How do I purge an entry from the DataSource table in the Activity database

SourceOne will not recognize three user accounts no matter what activity I create against their accounts. It works for all other accounts.

In looking at the logs I can see that there is an error accessing the DataSource table in the Activity database when I run activities that involve any one of the three accounts. I looked at the table and have found that of all the entries in this table, the three accounts that I am having problems with are the only ones duplicated.

So my quest is to either delete each users extra entry or just delete both. Can Someone tell me how to safely remove these entries?