Unfortunately, there is no easy way to accomplish this. As usual, if there is a will there is a way, but there is nothing supported or some way that I can think of that does not require quite an effort.

Thanks Linus:

My only thoughts on this is finding the correct UI file or JavaScript file to edit, and write some JavaScript to just "hide" it..

I have written something, but just can't find which file I should edit (I think it’s somewhere inside appdata\Modules, but whatever I edit doesn't seem to affect what I view..

I'm wanting to run

$(".dijitReset.epi-tooltipDialogMenu.epi-menuInverted tr:last").hide(); (or a pure JavaScript equivalent)

The above hides the button when run in the console.

I added to one of pages, but it doesn't work, as the page loaded inside an iFrame, so separate to the rest of the UI...

Any tips?

The UI and the site runs in different frames. If you want to execute JavaScript in the UI layer you need to create a shell module that starts your script. There is a module in the Alloy sample packages. This blog post describes how to set up an initialization module on the client:

http://world.episerver.com/Blogs/Linus-Ekstrom/Dates/2012/11/Creating-a-more-advanced-property-editor/

Add the following configuration under the clientModule section in your module config file to run this module automatically after the CMS module:

<moduleDependencies>
<add dependency="CMS" type="RunAfter" />
</moduleDependencies>