For example, "WARN [Reverse Replication Processor] com.day.cq.replication.Agent.publish_reverse Reverse replication not implemented for action: TEST. Remote outbox path: /var/replication/outbox."
The repository grows fast (several MB per minute), and logs show an error about reverse replication.
On the publish instance, find and delete the item from the publish box manually.
To avoid this issue in the future, either upgrade to CQ 5.6 or don't use the Test Connection button on the reverse replication agent.
Check with Adobe Support for an existing hot fix if you're having similar issues with reverse replication. (Also see the recommended list of hot fixes for CQ 5.4.)