Buildship is using Gradle v2.2 but it is not clear why or how to change

You don’t have to install anything manually. If you use the Gradle import wizard you’ll find the Gradle distribution selection on the second page. There, you have the option to use the Gradle wrapper from the project, or to use a specific Gradle version. In the latter case Buildship will download the distribution for you and associate it with your project.

Alternatively, you can upgrade your wrapper from the command line and then import it into Eclipse.