Running our Gradle build script on a traditional slave does some console output in which lines on the bash are often refreshed to show the current status of downloads for example. In Jenkins' job output only the final line content is shown.
Running the same script with the same job in a Docker container using this plugin, the console output in Jenkins shows the old and refreshed line content as well as the control characters to refresh the lines.
Example output run on native slave (or alternatively manually in Docker container):

00:00:23.307 :our.project.ear:cleanUpdateExternalEarLibs UP-TO-DATE
00:00:23.313 :our.project.ear:cleanUpdateExternalEarModules UP-TO-DATE

Same step run in Docker container using Docker Custom Build Environment Plugin:

13:34:35  [1m> Building 0% [22m [1m > :our.project.ear:cleanUpdateExternalEarLibs [22m [55D [0K [13D [0K:our.project.ear:cleanUpdateExternalEarLibs 
13:34:35  [1m> Building 0% [22m [13D [0K [1A [53C [33mUP-TO-DATE [39m
13:34:35  [1m> Building 0% [22m [13D [0K [1A [63C
13:34:35  [1m> Building 0% [22m [2D [1m1% [22m [1m > :our.project.ear:cleanUpdateExternalEarModules [22m [58D [0K [13D [0K:our.project.ear:cleanUpdateExternalEarModules 
13:34:35  [1m> Building 1% [22m [13D [0K [1A [56C [33mUP-TO-DATE [39m
13:34:35  [1m> Building 1% [22m [13D [0K [1A [66C

Executing the docker exec command manually on the host prints the lesser output of Jenkins jobs running on native slaves.