Symptoms
I deleted the test instances of the list items in my apps list.
The k2 worklist is still populated with items added to it that were these items in the list.
How can I delete or clear them from the k2 work list?
Diagnoses
Deleting or manipulating the list items from the sharepoint list that you have appified will not stop the workflow that is creating the worklist items for a user and also the list items are not tied to delete worklist items when they are deleted. If you want to remove those items to be actioned from the worklist you will have to stop the instances of that workflow or action those items to delete them.
Resolution
Go into the K2 Management page in the K2 for Sharepoint App and close the open instances of the workflow related to the worklist items that you would like to eliminate.
Another option is to action those worklist items but this still means that there is an unused workflow process hanging around that will never be used again. Not going to cause extreme problems in your environment but will just add unnecessary clutter and use resources that aren't needed. It is recommended that these unused instances be deleted.