There isn't one-answer-fit-all solution.
You should watch that links and sites for sure. For now keep them as-is. There are many old, authoritative and trusted directories in web. Examples can be found easy - Yellow Pages, DMOZ, Yelp, etc. So you should watch not only your links but also whole directory for spammy submissions, anchor text modifications, new links, spammy changes, etc. This can be the moment when directory will be turned into toxic asset and links can become bad. You should also watch for unusual changes - example i know software directory with links for "insurance in NY". Because site change this owner and new one start selling links with anchor.
This is why i cannot give you advise based on your question. But you should see some statistical numbers (DA/PA/Spam/Alexa/TF/CF/Ahrefs/social shares). You also need to see few pages of site and then you can know is site good and bad.