I recently designed a website for a client who in the past had used a link building company to get reciprocal and one way links and did so in a way that led to her website ranking dropping dramatically.
Is there any way that old links coming into her site will still cause damage? There doesn't seem to be any way that she could realistically remove these now.
Actually, you could ask each website admins to remove external link they have for your client's website, but that is a hectic process and cannot guarantee removal. Instead you can start getting valid and reputed external links to the website which would ultimately mask the bad links. Try getting links from top 10 websites in each domain or sector.
I agree with Timesheet. Trying to get the "bad" links removed is likely to be an exercise in frustration. In many cases, you'll have no way of contacting the sites concerned. And, if you do contact them, chances are that most of them won't take any notice of your request.
Nobody knows this for sure, but I strongly suspect that we worry too much about these supposed bad links. Despite what we've been reading recently, I can't imagine Google downgrading a site merely because of something that is outside the site's control. It would be different if you had entered into a reciprocal link arrangement with these sites, or if you were seen to be promoting them in some way, but I assume that's not the case here.
Better to put your efforts into getting high-quality links - and, of course, in developing the best possible content, so that other sites will want to link to you in the first place.
Another option you can consider would be to move the content to a new page for the links to pages you want to remove. Then you would let the old links you want to remove go to a 404 page. Google mentioned this option a few weeks back. It is not the best option, but one you can consider.
If you mean to ask if those links would "still" cause damage? Well, since you say that the damage has already occurred therefore there is no probability that there would be any additional damage, unless until you further create such "bad links". As mentioned by others, you should now consider building your authenticity by getting quality links.
I would agree it is not a very good solution, but if the bad links are hurting your site more than the good ones, it is something to consider. Personally, I would only ever do this as a last resort, and even then I would be hesitant to do it.