You would need to remove the data from the field. Reference Manager will just output the information in the DOI field and as part of an export that [pii] will be imported in some cases. So whatever you do not want to see in Word would just have to be removed in the database.
You can use the Find/Replace under the Edit menu in Reference Manager to globally remove that information from the DOI field in all references.
I would make a copy of the database first since there is no undo to the Find/Replace.