Links pointing to your website from sources with low quality trust and authority scores have a negative effect on your page rank. The cause may be due to your SEO agency using black hat tactics to accrue inbound links or the links could be spam.
However, that does not mean to say that all inbound links pull your website down. Relatively new websites that are still building up trust and authority scores with search engines could have genuinely linked to your site.
If this is case, you may want to consider keeping the link as it will positively boost your website once the host builds up healthy metrics. Before you decide whether to stick or twist, assess the quality of the content.
If you feel the host is publishing good content which is relevant to your industry, it is better to retain the link. It is only links from low quality sites that are producing poor content and spamming third parties that you need to lose.
Disinfection and disavow
When Google identify links pointing to your website that look “unnatural” they will notify you through Google Webmaster Tools. If the link is from an unknown source and is low quality remove it.
However, if the link is a potentially strong link, you can use Google’s disavow tool which ignores the link and allows your website to function as usual. But because the search engine removes you from rankings until you clean up bad links, it is best practice to periodically clean the backend of your website.
Clean-ups can be time consuming to perform manually, but with a Link Disinfection tool you can dramatically reduce this admin time. There are plenty of good tools available from the internet.
If you have employed an SEO agency in the past and have a lot of inbound links pointing back to your site, the chances are they were acquired contrary to search engines guidelines.
If that is the case you probably have a lot of links to tidy up whereby a disinfection tool will save you a heap of time. If you wait for Google to notify you of suspicious link activity, the search engine will disqualify your website from search rankings until you have cleaned up artificial links.
To protect yourself from being pulled out of search listings, periodically check inbound links to make sure they are from either high authority sites with healthy trust scores, or from sites that produce good quality content and has the potential to boost your rankings.