Not sure if you're referring to the 'sculpted' shape of the seat or what appears to be scratches on entire seat.
Looks like someone was sliding their behind across the seat so they could slouch on it. Do not let people do this as they break the backs of the chairs. Could be the metal studs on jean pockets that caused the marks. Only way to get rid of them is lots of sanding and re-staining. I would just leave them and ban that person from sitting in them.
Those are scratches, fortunately they haven't went through the finish. I agree, probably some embellishments on someone's jeans. You could try putting down a towel, and using a steam iron. I have had good results. Be patient with the process.
Thank you all for the ideas. I appreciate your taking time to comment!
What you can try is a damp cloth over the dents and an iron set on low. May just raise the grain.