Years ago, a template developer called me on a Sunday evening a bit in a panic. He had links in his templates and it had become a significant problem. I was using one of his templates and that is the reason why he was calling.
He explained that he worked full time and only did the template business on the side to help pay for his wife's medical bills. He continued that the decrease in traffic is really effecting his ability to make additional money and it was having a real effect. He explained that it appeared that Google was penalizing sites that are the target of template links and he was calling, e-mailing, snail mailing anyone he could. He explained that he thinks that changing the link to a citation would be okay.
I decided to help him and stayed in touch for quite a while after that.
In the end, converting as many links to citations as he realistically could really did help and the problem was resolved relatively quickly (a few months). He began to gain full traffic between 6 months to a year.
Warning about Manual Actions
The manual action was designed to inform you if a person has reviewed your site and has issued a penalty. Since then, a few automated penalties have been added. The up-shot is this. Do not think this page/option will tell you if you have a penalty. If you do, you will be sorely disappointed. Google will e-mail some found issues, however, for penalties, I have found that Google is extremely silent and not very helpful. Even for the innocent that Googles says it understands.
There has been a shift since Matt Cutts has left his position. Whoever the new person is, it seems that they prefer a hammer over any other tool. And that is a shame. In fact, it is annoying. Honest webmasters will work hard to remain within a reasonable scope that Google has historically defined. However, if you (Google) are not talking to us, or relying upon your vague guidelines, then you will be damaging yourself as well as others. This is a partnership afterall!
Google says (https://support.google.com/webmasters/answer/66356):
Any links intended to manipulate PageRank or a site's ranking in
Google search results may be considered part of a link scheme and a
violation of Google’s Webmaster Guidelines. This includes any behavior
that manipulates links to your site or outgoing links from your site.
The following are examples of link schemes which can negatively impact
a site's ranking in search results:
Widely distributed links in the footers or templates of various sites
There is some level of valid argument on this site when and whether a templated link will hurt. It appears that there are cases where a templated link will not hurt though it is limited. I do not believe this is your case- unfortunately.
I do explain what I have found to be the thought process for Google and the so-called toxic link. Keep in mind that Google, at the time of writing, did not use the term toxic link. You can read that here: What is a toxic link? It may help to at least understand the process.
Here, https://support.google.com/webmasters/answer/2648487?hl=en, Google warns about disavowing links. Here is the warning.
This is an advanced feature and should only be used with caution. If
used incorrectly, this feature can potentially harm your site’s
performance in Google’s search results. We recommend that you disavow
backlinks only if you believe you have a considerable number of
spammy, artificial, or low-quality links pointing to your site, and if
you are confident that the links are causing issues for you. In most
cases, Google can assess which links to trust without additional
guidance, so most normal or typical sites will not need to use this
It has been my experience that Google understands that links are created beyond the website owners control and that much of the time, a site should not be penalized. However, with the more recent updates, it appears that where the line is drawn may have changed. I am not sure where that leaves us just yet. It is just too soon to say.
What to do?
Since your theme/template contains a back link that is against Google webmaster guidelines, I suggest seeing if you can clean this up. It may be that you can use your Google Search Console (Webmaster Tools) account to see what back links Google is aware of. You may want to export this data into a list or spreadsheet. You can also do a search for a quoted key phrase that should find sites that use your theme/template. Compare the results with your list and begin seeing who you can contact using whois. Formulate a kind letter explaining your need to convert the link to a citation or having the link removed entirely. Wait to see what results you get.
If you are not having much luck, then stop. There is no sense going down a dead-end street.
The next step is to determine what sites are likely damaging. For example, foreign language sites, low quality sites, spam sites, etc. Keep note of these in your list and only disavow those sites that are particularly egregious. Do your work slowly and in phases. It can take a long while before Google fully realizes what has happened and begin to correct the trajectory for your site. This means you are in it for the long haul.
In the end, you can fix this. I would not fully abandon contacting webmasters trying to get your links converted. This will allow you to shorten your disavow list. I imagine that there is a point where effort versus payoff will dictate how and what work you do. However, I also argue that reducing the need for disavow is your larger goal.