Their job is greatly complicated by the fact that animal cruelty - serious animal cruelty - does not appear to be taken seriously by the island's administrators at all.
Over the last two years, a local sadist (possibly more than one) has been regularly poisoning the cats at Pollonia, one of the larger towns on Milos. He or she puts snail bait or animal fertiliser in fish and leaves it for the cats to find. On the last occasion over forty cats were killed.
In Australia, or the UK, or the US, or any number of other countries where humane legislation has passed criminalising animal cruelty*, this would be a serious crime and the police would allocate resources to finding out who did it and making sure they don't do it again. On Milos - not so much. It's "not a priority".
Which is odd, because the Greek islands' cats are quite a tourist drawcard. All the tourist advertising we've seen regarding the area features the feline population quite extensively, and the souvenir shops are full of postcards, calendars, t-shirts and other comically overpriced paraphernalia covered in Greek cats. If we hadn't already massively stocked up on "I Gatti di Roma" stuff in Italy, we'd almost certainly have failed to resist buying unnecessary amounts of it on Milos.
We may possibly have visited these kittehs more than once.
But the island authorities don't give a stuff that there's at least one nutter out there killing the creatures. Poisoning them, so they die in an particularly painful manner. In fact, there are some suspicions that the council itself may be involved.
And while that situation exists, I wouldn't blame any compassionate, humane person from giving this beautiful island a wide berth. Attempting to encourage the island's traders, dependent as they are on tourism, from pressuring the council and police to bloody well enforce the law. And sending any assistance they can to the Milos Friends Of The Animals.
The sooner they can bring an end to the stupid, inhumane slaughter, the sooner Milos will be a place one could recommend visiting.
PS On the last night we were on the island, a dog was found hanged.
*For one thing, the nutters who delight in causing pain to animals tend not to stop at animals.