Legal Question in Business Law in California

If those are the complete facts, it is not legal for them to do. If they gave a quote, which you accepted, they did the work, they invoiced you the quoted price and you paid it in full, that's the end of the story. It's way some construction subcontractors who work with supplies and materials that have volatile prices give contingent quotes, with the cost of materials being subject to change, or they quote a "not to exceed" that covers the highest estimated cost of materials. Absent that kind of quote and agreement, your vendor is stuck with the price they quoted and you paid.

They may claim they made a mistake, which is a legal reason to void a contract and excuse performance, meaning that they could have refused to do the work. But they went ahead and did the job at the rate they quoted and which you paid in full. In practical terms, they would have had to get the supplies before they created the work for you and must have known then how much it would cost, unless their vendor mis-quoted them. It seems that their claim should be with the vendor, not with you.

They also have the issue of making a false claim against you for a debt you never agreed to, which may violate collections laws.

You really should take all your paperwork to a lawyer as soon as possible because, unless you handle this correctly, you might screw up your credit and cost yourself more money.