Hi Kathryn. I totally appreciate your viewpoint on editing files, however so long as you follow the guidelines laid down in our Themer’s Guide (link on the right, under Useful Resources) you should be ok – as your customizations will be stored separately from the core plugin and unaffected by The Events Calendar updates.
If you want to remove those buttons, you can do! Once again please refer to the Themer’s Guide for the background to this – but what you will be looking to remove from the relevant custom templates are template tags such as:
tribe_get_listview_link();
And also:
tribe_get_gridview_link();
For example, you can find this block of code in gridview.php – http://pastebin.com/s2QcBrn2 – if you simply remove it (from your custom template that is) then the buttons will no longer be present. Does that help?