You can hide (or filter out) the connection status if you do not want to see the status either on the individual connection icon or as part of the rollup status for Replication Server.
Hide the State of the Replication Agent –– hides the state of the Replication Agent thread in the Details list, on the Connection Properties dialog box, and in the rollup status for the Replication Server to which that Replication Agent thread is connected.
Hide the State of the DSI Thread –– hides the state of the DSI thread in the Details list, on the Connection Properties dialog box, and in the rollup status for the Replication Server to which the DSI thread is associated.
To hide the connection status: