You can sue them: that is how you get compensation for damage negligently (e.g. carelessly) done to your property. A good option would be to sue in small claims court, as your own attorney, which will minimize costs and get you into court faster. You will need to testify about and/or provide other evidence (e.g. photographs of the carpet before and/or after; invoice or bill to show when they did the work; etc.) the fact that the damage was done by them and prove to the court by a preponderance of the evidence (that it is more likely than not) that they are responsible. If you can do that, you can get a judgment in your favor requiring them to pay for the damage.