Remove deprecations usage in `docker` provider system tests (#39487)

diff --git a/tests/always/test_example_dags.py b/tests/always/test_example_dags.py
index 3a0d947..427af8d 100644
--- a/tests/always/test_example_dags.py
+++ b/tests/always/test_example_dags.py
@@ -52,7 +52,6 @@
     "tests/system/providers/amazon/aws/example_emr.py",
     "tests/system/providers/amazon/aws/example_emr_notebook_execution.py",
     "tests/system/providers/dbt/cloud/example_dbt_cloud.py",
-    "tests/system/providers/docker/example_docker_swarm.py",
     "tests/system/providers/google/cloud/azure/example_azure_fileshare_to_gcs.py",
     "tests/system/providers/google/cloud/bigquery/example_bigquery_operations.py",
     "tests/system/providers/google/cloud/bigquery/example_bigquery_sensors.py",
diff --git a/tests/system/providers/docker/example_docker_swarm.py b/tests/system/providers/docker/example_docker_swarm.py
index 88a200b..6546c7d 100644
--- a/tests/system/providers/docker/example_docker_swarm.py
+++ b/tests/system/providers/docker/example_docker_swarm.py
@@ -38,7 +38,7 @@
         docker_url="unix://var/run/docker.sock",  # Set your docker URL
         command="/bin/sleep 10",
         image="centos:latest",
-        auto_remove=True,
+        auto_remove="success",
         task_id="sleep_with_swarm",
     )