Who is responsible for the cost of this repair?

My husband had arranged for a septic tank cleaning which was done early this afternoon. Long story short: The company that did the cleaning of the tank backed their large, heavy truck into our driveway to gain access to the tank in order to pump it out. I don’t know how it happened, but the truck had crushed a section of the asphalt in our driveway and now it is a huge mess. I would say the damaged area is about 10 feet long and a few feet wide. Its ruined in that entire area. They also damaged some of the lawn area on one side of the driveway while either backing up, or pulling out of the yard, leaving a rather wide strip which is nothing but a large rut of dirt now.
The owner called not long ago and offered to come and pick up the broken asphalt, but made no offer to repair it.
The driveway, and the lawn were in very good shape before they came here. Now, both are damaged. The driveway is my main concern. My question is: Who is responsible for the cost of repairing the damage? Is it the company that did the damage, my home owner’s policy, or will we be stuck with the bill ourselves?
Thanks for any suggestions/advice you may have.
Neither of us signed any papers with this company. I simply left a check out on the front door as payment for their services. There were no work orders or any other documents signed by either one of us. It appears to be the sewer company’s responsibility to repair the damage?
BTW, thank you for your answer!

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