My Smartsheet Contacts vs Group Management

In using the Assigned To column, I found that several Contacts did not have their First and Last name fields populated.  So, I went into My Smartsheet Contacts and updated all of my Contact items so that all have their First and Last name fields set.  I then saved the sheet, closed it, reopened it and went back to the Assigned To column.  I once again found the entries *without* their First and Last name fields populated!  In evaluating the issue, it seemed to me that the Assigned To list was being populated from the list of persons I had shared the sheet with, not from My Smartsheet Contacts as I initially assumed.  I am sharing the sheet via a group, so I went into Group Management and found the Contacts were missing their First and Last name values!

My question then is how to manage the Contact items in a Group?  My assumption was that when I updated the Contact items in My Smartsheet Contacts, that the Group would have pulled from that to update those Contacts also.  However, it appears that each Group is using a wholy separate list of Contact items stored independently from My Smartsheet Contacts.  The only option I see is to remove each entry and readd them.  However, that will span unwanted emails to those persons.  How can I work around this?

Screenshot of My Smartsheet Contacts showing the fully populated Contact item: