While digging through my registry, I found the following entries:
[HKEY_CURRENT_USER\Software\giveawayoftheday.com\wrapper2]
"SiWasInstalled"=dword:00000001
"SiWasOffered"=dword:00000001
It seems the wrapper keeps track of if Software Informer was installed or not. The second entry will stop prevent the wrapper from asking you if you want to install Software Informer, and the first will hide the Install Software Informer button on the Activation Successful screen, and it also does what the second entry does.
So... to prevent the installation of SI by the wrapper, if you haven't clicked no on the prompt, copy and paste the above entries into a text document(from the "[" to the last "1"), rename it into a .reg file, double click it, click yes to insert info, and you will have no prompts or install SI button the next you run the Giveaway wrapper.
The wrapper doesn't check if SI has been uninstalled.
(Background info: If you click no on the SI prompt, the wrapper creates the second entry; if you click yes on the prompt, the wrapper creates the first entry, but not the second, and hides the Install SI button. If you click no on the prompt but do click the install SI button, you'll have both entries.)