Is it permissible to harm a neighbor in retaliation for his harm and his disregard for the complaints of those affected by the noise from his workshop, especially in the absence of a legal deterrent?

It is not permissible for a neighbor to harm their neighbor, and the harm must be removed if the neighbor does not forgive them. The affected party should strive to resolve the issue amicably. If amicable attempts fail, they should refer the matter to the competent authorities to remove the harm through peaceful means. It is not advisable to harm a neighbor.