The NHBC seem to be trying to fob buyers with defective homes, with a cash offer for them to go away and either live with it as is, or get the works done themselves with everything that entails.
You would need to read the small print on your warranty policy as NHBC may have opted out of arranging for the works to be done.
One thing that always applied is the defect if not properly rectified first second or even third attempt stays on the books and is covered under the warranty until it is resolved. Again NHBC may have changed this too!
New home warranty is after all, an insurance policy. Insurers hate paying out claims.
But you can take a complaint to the Financial Ombudsman Services (as many do re new home warranties)
Please do this if you are not happy as there is a permanent record of all complaints to the FOS so when new home warranties come under the spotlight as not working as they should, perhaps the government will act.