You had to take it back to Cartier to get the lipstick refilled, and you held onto it with a little ring or chain that hooked over two fingers.
There was no way to get it refilled. 
mnli hypothesis: There was no way to get it refilled.  premise: You had to take it back to Cartier to get the lipstick refilled, and you held onto it with a little ring or chain that hooked over two fingers.