How to parameterize the choice of whether to do a clean build?

A default Teamcity build has a checkbox for this parameter, so I cannot parameterize it directly, right?

It seems like the Gradle  plugin might enable me to parameterize the choice of whether or not to do a clean build, but I cannot see how I should use it?
So far I see I can choose Gradle for a build step, but then I'm unclear how that relates to choosing yes/no to do a full checkout or merely an update.

Possibly I am all mixed up and Gradle is not the tool to use, so I look forward to your tips!