...just another thing to ask your lender about.
If I can be of any further assistance, please don't hesitate to contact me at http://www.HernandoLuxuryHomes.com - I'm always happy to help.
Next I would prefer to do any work that I was going to live with myself. Put in the carpet.
Second item: If the sellers are paying for carpeting, the value will be deducted from the maximum amount of your closing costs paid by the seller. But as Joshua pointed out, your lender may not accept the condition of the property if the bedrooms are unfinished.
Third item: Are the sellers paying cash at closing for your closing costs? If no, you are either paying the closing costs out of your down payment or finanincing them in your loan. Sellers typically fund the buyers' closing costs at the funding table from the proceeds of the sale.
Fourth Item: Your Good Faith Estimate from your lender or broker will show you your total cash-to-close and your net cash-to-close after deducting seller contributions to closing.
Keep in mind that carpeting is not a significant "problem" with a home. Provided that they are not selling you a house that needs actual repairs, the carpeting allowance may seem petty at this point and invites animosity from people who presumably still have keys to your recently-bought house.
The key to this negotiation is that the carpet is not included in the written contract, and you probably don't want to try convincing a small-claims court that the seller is in breach of an oral contract. I recommend taking the money you would have put into closing costs and using some of it to select carpeting that you'll really enjoy, and waste no more angst over this unwinnable disagreement with the seller.
If I can be of any further assistance, please don't hesitate to contact me at http://www.HernandoLuxuryHomes.com - I'd be happy to help however I can!