If you want to disable the Like function entirely then you can do that by disabling the Confluence Like Plugin by following the instructions in this document: https://confluence.atlassian.com/display/UPM/Disabling+and+Enabling+Add-ons#DisablingandEnablingAdd-ons-Disablinganadd-on
However, this will disable the Like function entirely in your Confluence instance so I'm not sure if this would work for you because it disables it globally but it is certainly one solution for you.
All the best,
Specific to Zen Intranet...
The Like link and icon is located in the Labels Zen bin. You can hide this bin by editing the Master Page Layout.
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