Steps to reproduce:

1. Create a job
2. Switch "This build is parameterized" on
3. Add "JIRA Issue Parameter", fill "Name" and "JQL Search Query" fields
4. Run the job, select an issue for the parameter
5. Open the build page, go to "Parameters" - the issue ID is shown
6. Open the_build_url/api/xml - there is just the parameter name:

   <parameter>
     <name>JIRA_PROMOTION</name>
   </parameter>