Ask HN: Just got a C&D letter claiming trademark infringement..need advice

I'm looking for advice on a subject that I have no knowledge about and I'm hoping someone in the community can shed some light on the best way to proceed with this.

Myself and a partner registered a Canadian corporation last month called "Picket Fence Games Inc." We did a NUANS report (Company name and trade-mark search reports from Industry Canada) and it returned a blank report meaning there was nothing remotely close to it in Canada.

Last week we released our first game for the iPad titled "Animal Scratch for Kids" in the Apple App Store.

Two days ago we received a Cease and Desist letter from a US game studio that our company name is infringing on their US registered trademark (for International Class 9) of "Picket Fences" for goods or services in the computer games industry. They have proceeded to contact Apple that our company infringes upon their registered trademark.

The case they make is that their "Picket Fences" trademark is very similar to our "Picket Fence" company name and that the word GAMES in our company's name and website must be disclaimed from a trademark perspective because it's the generic term for our company’s underlying products.

We never intentionally meant to dilute the brand name of one of their games by naming our company as such nor did we know that we were infringing on a trademark. I know that in legal terms the above statement means nothing but I just wanted to say this wasn't done on purpose in order for us to benefit from their success in any way.

Our money as a small startup can be spent in better ways than dealing with the legalities of this issue so my questions to you guys are:

Do we realistically stand a chance of wining this case against this company? DO we even have a case? How do we make sure this doesn't happen again?

If this is the case for any trademark in the world and we are dealing with an App Store that sells to the entire world this would mean that any person in the entire world with a trademark could potentially shut down any company. How can we protect ourselves in such a case? Is there a world trademark search, and is it feasible to run?

Any help, advice or comments are appreciated. I left corporate Canada as a developer to do something fun and creative and get away from all the red-tape and legal crap and this just brings me right back...

Thanks,

Nik