how to remove the .squarespace from my domain

I originally started with Squarespace on v 7 and then rread that I couldn't simply transfer to v7.1, I needed to cancel my account and then rebuild under the new version. Now that I have done so, I can't seem to find a way to have my domain without the .squarespace extension. It seems that my original domain (without any .squarespace) is still out there, is this the reason? How can it be resolved...any ideas?

The .squarespace.com domain ending is the built-in domain for accessing your website, it's not something you can remove. What most people do is have a custom domain name connected to their website which then acts as the primary domain name for your website visitors. It sounds like you haven't disconnected your custom domain name from your 7.0 website and connected it to your new 7.1 website.

Have a read through of the guides Squarespace provides, and if that doesn't help you enough, then you could ask Squarespace Support to help you via their live chat:

https://support.squarespace.com/hc/en-us/articles/205812088-Domains-basics