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If you have to pay a fee to get listed in a directory, then some might consider that to be a purchased link.
If the website is paying for editorial staff to review the site - and therefore the entry can still be turned down if it's not up to editorial standards - that is NOT considered a paid link. If the directory accepts every site that pays them, then that IS considered a paid link.
...If the linked to site has disproportional percentage of keyword anchor text in its inbound link profile, it is a case for it to remove such links or edit link anchor text where possible. Again, if the directory is not in the habit of giving Title just made of keywords, I don't see a reason why should they be removed.
...Again, if a directory has stuck to its editorial integrity and not compromised on categorization or placed RoS links to Payday Loan sites, that directory can't be on ones hit list.