I don't have any videos on my page and I don't plan to change this anytime soon. Is there any way to remove the link?
In Manage Tabs » Add or remove tabs I can only add apps but not remove or disable the Videos tab.
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I'm not aware of a way of doing this directly. However, you can use the plugin from Social Fixer.
This enables you to turn off and/or hide several "features" of the Facebook page like this.
It isn't available for all browsers on all operating systems but it covers most combinations.