I have a parameterised build that accepts a number of parameters using the 'list subversion tags' parameter type.

Once the build has completed (successfully or otherwise) I can go back into the job in Jenkins and review the values that were set for the parameter in the ui.

However if I download the job information via the api (json or xml), it only lists the parameter names, and not their value. I have other parameters in the job as well, these do come out through the api.