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You wouldn't have any legal recourse against the city because: i) they have immunity; and ii) they did nothing to really cause the problem; rather, they are simply following their guidelines and could justify their actions based on their rules and regulations which are designed to protect the safety of homeowners. BUT, you absolutely do have recourse against the contractor for any and all damages you are suffering due to his failure to perform, which would include any lost savings in interest paid due to being unable to refinance the property without this lien. You should send him a certified, return receipt requested letter detailing the situation and his default, and demand he pay you the full amount any and all damages you suffer due to his default. Inform him that if he does not timely comply with your demand, you will have no choice but to file a suit for your damages. BUT, be sure to specifically mention that you will be filing this claim not only as a breach of contract case, but also be including a claim of intentional misconduct, which will entitle you not only to your damages, but also an additional amount equal to multiple times your actual damages as punitive damages. That should provide plenty of incentive to comply with your demands; but, if it does not, file your suit. Even if you have to file the suit, that's likely all you will need do. In my experience, he will settle this without a hearing rather than risk punitive damages and the judgment being on the record.
Now, going back to the city, it's possible if you contact your city council person, you can work out a solution to getting this lien released upon signing an agreement regarding any further work on the basement without obtaining proper permits and inspections.
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