Story status displays "com.ibm.team.apt.story.verified" instead of "Done"

review the work item's workflow, it should tell how verified state is reached
Open PA in Eclipse Client > Project Configuration > Configuration Data > Work Items > Types and Attributes > Select a Work Item Type from Work Item Types section > Workflow > Click on the Pencil

for your case, i assume a resolution action was associated with one of the actions :
 
Look at the Actions and Target State section, Select possibly the Verify Action which is associated with a resolution, you might find one of the resolutions as com.ibm.team.apt.story.verified

moreover, IDs get displayed when there is a reference to a deleted artifact.  So unless you have a state or a resolution named com.ibm.team.apt.story.verified, this might correspond to a deleted state or resolution.

hope it helps

In addition to the info Dinesh provided above, I would also try the following...

1. Select to 'Synchronize attribute' on the story item in problem

2. Try to change the workflow state (select any workflow action to move it to a valid state, if possible).

The state Id's are mapped to their state name from the work item type's workflow. 
If this mapping fails, the ID's show up.

Below are the possibilities where the mapping (match) fails on existing work items and ID shows up:
-  work item was transitioned to a state and later that state was deleted from the work item type's work flow
-  work flow for the work item type has changed and in the new work flow, the state id does not exist

You can look at the configuration source for the work flow definition and the ID's of the states.

You would need to map that state to a proper state from the latest associated work flow to resolve this.
This mapping can be done with an Export (ID and Status) of the problematic Work Item and update through a Re Import ( ID and Corrected State ID).