Check out the link_to documentation - I this will describe what you want.
I haven't tested this, but I'm guessing you want:
<%= link_to "delete", controller: 'favourites', action: 'delete_from_index_list', id: @favourite, remote: true %>
If it were my code, I would find the route for the delete_from_index_list
method, and call it this way:
<%= link_to "delete", route_for_delete_from_index_list_path(@favourite), method: :delete %>
This way it's more resourceful, whereas the former example is non-resourceful.