That is (as far as I know) the way FM works standard with table view. I only use "table view" for myself as developer and check data. For users you should build a "list view". In list view you can create buttons, and hide buttons the way you like it.
But, also in table view you can use "previous version" (record) to undo the unwanted record. (You even can built a button for that function).
In FileMaker Advanced, You can install a custom menu that does not have the New Record menu option and then no one, not even a full access user, can add a new record on this layout. (though full access users with FileMaker Advanced can temporarily install the standard menu and then they can create a new record. If you want the users to be able to add new records you can set up the view option for table view inside Layout setup to show the header and put a button in the header to perform a script to create the new record.