I believe that AMEX tracks bonuses carefully, but, if you applied through this offer, you would be entitled to any bonus points above the amount of bonus points that you received in a previous sign-up bonus.

Example, if you previously applied for AMEX *wood in 2005 and received 4K sign-up bonus, you would be able to apply again and get 2k bonus. If you are still a current card holder, don't know if you have to cancel existing card first. This is based on FT threads that I have read on this subject.

As an alternative, try the following. When I signed for AMEX *wood, sign-up bonus was 4k, and I was not aware of 6k offer when I signed up. After second statement, I called AMEX and asked about 6k bonus, and they gave me the difference without any argument. ^

You may need to have some spend for them to give up the extra points, though.