I don't get why you need to log into Gmail to invite people to a web site, why not just give them the address?
Example: Hey Newgeek1 wozzzz up, check out my site it's http://www.geekstogo.com
Or have I misunderstood?
The error you are getting usually comes about when you log in from a foreign location into Gamil IE not your usual IP. Open Gmail and scroll to the bottom of the page click recent activity and check the IP's listed, if you see odd ips that are not yours check them out by copying them into a google search and using a site like http://www.ip-adress.com/ip_tracer/
to get info on the ip. If it turns our these are not your IP's change your Email's password as somebody has got your password by whatever means (there are a few ways they could have done this). Before you change your password make sure in settings that emails are not being forwarded as this is a little trick some hackers use to steal emails and do a full scan for malware, for this you will need to post a log into the malware section on this forum as I'm not staff here I can't help with this. All that said this last bit only applies if you have noticed unusual activity in the recent activity section of your Gmail.