Thanks for the answer.  Yes.  I know that you cannot do it with a workflow rule.  I am trying to do it with a trigger or batch apex.  

I was thinking that you could have a trigger like this on the account...

trigger deleteOld_Owner_tasks on Account (before update) {
   
        Set<Id> accountIds = new Set<Id>(); //set for holding the Ids of all Accounts that have been assigned to new Owners
        Map<Id, String> oldOwnerIds = new Map<Id, String>(); //map for holding the old account ownerId
        Map<Id, String> newOwnerIds = new Map<Id, String>(); //map for holding the new account ownerId
        Task[] TaskUpdates = new Task[0]; //Task sObject to hold OwnerId updates
       
        for (Account a : Trigger.new) { //for all records
            if (a.OwnerId != Trigger.oldMap.get(a.Id).OwnerId) {
                oldOwnerIds.put(a.Id, Trigger.oldMap.get(a.Id).OwnerId); //put the old OwnerId value in a map
                newOwnerIds.put(a.Id, a.OwnerId); //put the new OwnerId value in a map
                accountIds.add(a.Id); //add the Account Id to the set
            }
        }
       
        if (!accountIds.isEmpty()) { //if the accountIds Set is not empty
            for (Account act : [SELECT Id, (SELECT Id, OwnerId FROM Tasks) FROM Account WHERE Id in :accountIds]) { //SOQL to get Contacts and Opportunities for updated Accounts
                String newOwnerId = newOwnerIds.get(act.Id); //get the new OwnerId value for the account
                String oldOwnerId = oldOwnerIds.get(act.Id); //get the old OwnerId value for the account
               
                for (Task t : act.Tasks) { //for all tasks
                    if (t.OwnerId == oldOwnerId) { //if the task is assigned to the old account Owner
                    delete t;
                    }
                } 
          
            }
           
        }
  
}


It did not work.