The idea that putting things right will protect your reputation is not right in my opinion, you will always be the company that ruined thier carpet whether you replace it or not.
And thats what they will tell thier friends, they will say " he ruined our carpet and had to replace it" not because your are so professional but because you are crap.
Once you make a c0ck up your reputation has gone you can put things right but don't think for a moment you have repaired your good reputation with that customer..... They only remember the mistake you made