From my point of view the plugin should not consider the installed tools at all if gradle wrapper is selected. If created a pull request here: https://github.com/jenkinsci/gradle-plugin/pull/23

Are you manipulating the Gradle build step programmatically, or how can this issue be reproduced?

No, I'm not manipulating the build programmatically. I switched a build from a fixed version to gradlew like shown in the two screenshots attached. After the change, the gradleName property is still set in the config file. The current logic in Gradle.java is still trying to use the tool version, although it should use the wrapper and the gradle version that comes with it. See the attached jenkins-24682.zip file for a minimal example that fails with the current code and is fixed in my pull request.

BTW: A workaround with the current release is to to set the gradle version to default before switching to gradlew, but this is not really intuitive.

Code changed in jenkins
User: Mario Mohr
Path:
src/main/java/hudson/plugins/gradle/Gradle.java
src/main/java/hudson/plugins/gradle/GradleInstallation.java
http://jenkins-ci.org/commit/gradle-plugin/ace07ad4e0a801fcb3afb37a907b83b21586e3a7
Log:
[FIXED JENKINS-24682]

Jenkins gradle installations are ignored if gradle wrapper is selected

Code changed in jenkins
User: Gregory Boissinot
Path:
src/main/java/hudson/plugins/gradle/Gradle.java
src/main/java/hudson/plugins/gradle/GradleInstallation.java
http://jenkins-ci.org/commit/gradle-plugin/8730d78a456cad424db4061a272adb4b9631e9f3
Log:
Merge pull request #23 from mamohr/JENKINS-24682

[FIXED JENKINS-24682]

Compare: https://github.com/jenkinsci/gradle-plugin/compare/763256601be2...8730d78a456c