That's like saying that if Mark Zuckerberg had a MySpace account that they could sue him for creating Facebook. No-where in the terms of service does it say anything about creating a similar service, even my attorney agrees that there is no basis there.
"They suggest that your previous association with them gave them rights in certain intellectual property (presumably, copyright and/or patent) which you are using in your website. If your code is wholly original, they may claim copying if the design or approach is derived from a prior work they (or their predecessor in interest) created. However, that does not extend to the concept or ideas."
Maybe, but it looks like they figured out you had an account with them and they have a clause in their terms about intellectual property.
If your screens look similar they will try to hold you to that agreement. It doesn't look good.
At this stage you can back out with no costs, I suspect if you move forward they will try to get back their legal fees.