When adding "server-icon.png" to your server directory you can have a logo for your server now, and if you update that file a restart is needed to update the clients cache.
However, if you delete "server-icon.png" from your servers directory and reboot, the clients cache will not update, leaving the logo there. So, if you wanted to remove your logo you can't, unless you just upload a transparent image.
Linked issues
Comments 2
Duplicate of MC-34756
Is this still a concern in the current Minecraft version 1.7.4 / Launcher version 1.3.8 or later? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.