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.
Cartier would refill the empty lipstick cartridges. 
mnli hypothesis: Cartier would refill the empty lipstick cartridges.  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.