The carpet pieces are held on by three plastic clips on each. They slide into keyhole type slots on the back but I suspect you will have to push the clips out of the door card rather than try to unhook the insert from the clips because one of the slots goes in the opposite direction to the other two. Have a look at a picture of some to get the idea, e.g.
https://www.ebay.co.uk/itm/373905647002
I’ve never removed or refitted these myself. Those sort of fittings are usually ok to manipulate if you can access the back of them to push them out but often snap if you cannot.