I cook the food directly on the liner, with the liner placed on the hot plate.
I would not myself use one over exposed charcoal for fear the temperature involved there could release nasties from the PTFE.
Using the liner here would tend to defeat the real purpose of charcoal BBQing, the flavouring from the food juices burning on the charcoal
As an aid to cleaning the plate if that is used as the cooking surface. Pour a jug of water with a bit of added washing up detergent directly onto the plate after you remove the food, that helps stop the food juices remnants burning onto it and it greatly eases later cleaning it. I actually continue to do this even with a liner, it just helps reduce the effort later, making the whole use of these things less hassle, more enjoyable.