You cannot. Doing so is a violation. However, you can prevent anonymous users from making edits. To do so, go to Special:WikiFeatures on your wiki. Find "Require all contributors to log in" and enable it.
In addition, you can also lock the pages in question if you're an admin on the wiki by hovering over the down arrow next to "Edit" and clicking "Protect".
Another arguments against removing the Edit button is because you would be locked out of making easy edits too; and the people you don't want to edit could still do so by adding "?action=edit" to the page URL, unless it is locked.