Is it permissible not to return the ball to children who throw it into the home garden, and who cause annoyance to the homeowners with their shouting and exchanging of insults, after repeatedly advising them without a response?

If children annoy or harm neighbors, one should first complain to their parents to stop them. If that doesn't work, they can be deterred by sprinkling water or similar means. If the harm is not averted thereby, and the ball falls into the house, it is permissible to keep it until the end of their game and then return it. However, if their harm can only be stopped by destroying the ball, then it is permissible to destroy it, as this falls under the category of repelling an aggressor (ṣāʾil). In such a case, harm is repelled by the least severe means first; if it cannot be repelled except by the most severe (destruction), then it is permissible. Anyone who intends harm to a person, their property, or enters their home without permission has the right to repel them. An aggressor is repelled by the easiest possible means; if it cannot be repelled except by killing, then it is permissible. This applies to repelling animals, children, or insane persons if they assault one's person or property: if their harm cannot be averted except by destruction or killing, then it is permissible. However, if it is possible to repel them by a less severe method, then destruction or killing is not permissible.