Hiding old CRM Contacts in Desk

Hiding old CRM Contacts in Desk

I have an issue with contacts in Desk.   We sync contacts from CRM with DESK and we have old contacts, eg staff members that have left businesses.  The issue is when adding a ticket (most of our tickets are raised over the phone), staff sometimes pick the wrong contact from the list of available contacts.

In our CRM to desk Sync I am syncing only "Active Contacts" however it seems that the sync will not remove, or flag as inactive contacts that are no longer members of the view. 

Does anyone have a way of resolving this?  I don't want to delete the old contacts as I will lose their history.