What is the ruling on killing a feral cat that has caused significant losses to its owners by eating pigeons and eggs?

It appears that killing a cat by mistake incurs no sin, due to the Prophet's (peace be upon him) saying: "Indeed, Allah has forgiven for my Ummah their mistakes, forgetfulness, and what they are coerced into." It is permissible to kill it if there is no other way to get rid of its harm except by killing it, provided that it is done in a way that does not involve torture, due to the Prophet's (peace be upon him) saying: "If you kill, then kill well." It is permissible to kill male cats that eat meat and the like, such as vermin, and also if their harm cannot be averted except by killing them.