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After more than 13 years, and tens of thousands of questions, Moz Q&A closed on 12th December 2024. Whilst we’re not completely removing the content - many posts will still be possible to view - we have locked both new posts and new replies. More details here.
I believe the most reasonable action is to let them fix all your site issues and delete all irrelevant backlinks before you terminate the contract. So No, it would not be better to terminate them right now, but as soon as they fixed all issues you can terminate them ASAP and move on. Your website is very nice though, I showed it to my wife and she liked it a lot. Cheer up. 
You got it right Astrid. Don't ask them, ORDER them to do so.
You're welcome Astrid.
What I'm more amaze at is there are people who pay for SEO services without the basic understanding of SEO. I'm not saying this is the fault of site owners alone but their SEO providers too. SEO is a continuous investment, with this in mind, we need to establish good connection to our clients and in order to do so, we must be responsible when marketing SEO otherwise.
You're very much welcome Astrid,
But seriously, I laughed out loud when I read about your SEO provider claims. If that were the case then the more reason you don't need them anymore. How easy SEO could be if that were true.