It is a major nuisance: you pack your jewelry in the best possible way and still it gets deformed during transport. Is it possible for your customer to fix it without sending it back and running the risk of even worse damage?
Here is DYI advice on home jewellery repairs.
The trick is to improvise. Find a “mandrel” – a round shaped object which has approximately the diameter of your finger. It is important that it is made of metal or wood or any other hard material! Pull the ring over it, sometimes even pulling over the “mandrel” removes the deformation. Take a hammer – preferably a rubber mallet, but any hammer will do if you wrap its head in a cloth. And – very gently – hit the ring all around the mandrel. If you hit too hard the ring may grow in size.
P.S. Since I have encountered this problem several times, i.e. that pieces get misshaped during shipment, now I ship jewellery – and rings in particular – in gift boxes.