I've recently started working at a company with a moderately successful website. In the past, this company paid a SEO company to do work for them who purchased many low quality links for them. I'm trying to work at improving their rankings, and I wondered if I should be trying to remove these links and to what lengths I should go to removing these links. We have not received notices for our links, but I know that many of the links are bad. I've started contacting site owners to get these links removed, and thus far all the sites are charging for link removal. At what point should I start using the disavow tool? Should I be paying for link removal, or just go straight to using disavow? Or should I not even worry about getting rid of these links since Google hasn't seemed to take notice anyways?
Do any of you have any recommendation as to how I should approach disavowing as well? Should I add sites/pages to the file in increments and watch to make sure that it's not harming my ranking too much?