They can't really claim dibs on any name that happens to end in "oogle" and your firm does not seem to have anything to do with web search. Domino Sugar once tried to claim that Dominos Pizza was infringing on their name, a claim which they ultimately lost.
They've surely got the pockets to harass you and sadly you're going to need an attorney to respond to their complaint.
The "z" is a plural: "Sitez". Surely this meme, while old, can't be so old that only I remember it. Can it?
Meanwhile, let me introduce you to Google's website building business: http://sites.google.com
That's arguably in the same field of business -- enough to cause confusion in the marketplace, which is the legal standard -- and their URL is two characters away from the alleged infringing URL.
I guess this company could try to argue that Google is infringing their trademark... provided they launched before Google Sites, which came online under that name in 2008. Except, oops, the opponent is Google, a company whose legal team's lunch budget could probably buy and sell us all.
Run away!
The very worst that can happen is that I lose a few thousand dollars defending their contest. It's not like they are going to back down at this point. The next thing they'll send is the domain dispute letter. If I lose, fine, I'll change the name. But just instantly giving in to the big "do no evil" bully seems a little premature.