How can you check if someone is not building or redirecting a low-quality backlink to your site?

Hi Friends,
Plain and simple. You have to monitor your backlinks and rankings. Google webmaster tools for example is a free option you can use to check your backlinks, but they don't send you alerts - you have to keep checking your backlinks manually (as far as I know). There are plenty of SEO backlink checker tool out there as well that you can Google. There are also plenty of SERP trackers that will help you track your rankings.

As far as checking if they are building low quality backlinks - how are you defining low quality, what metrics are you using, etc.. This is a whole study in itself.