Hi bjc
I had a problem like this many years ago when my neighbours hammored large nails all sticking up with round 5mm tops down the tops of their fences which ran along side our side boundry. I did notice them until one day my beautiful Arnie (blue Bermese) came in and blood was dripping from his underneath. Took him straight down the vet who found two holes in to his fur bleeding and had to keep him on over night for x rays to see if any inner damage was done. Thansk fully no inner damage so he came home next day with stitches & antibiotics.
We (the vet & I) tried to find why he had two very similar holes in his underside and he though it must be a bite but very unusal. When i came home i looked all over the house and garden to try and think what could have made the holes in him and found the fences with nails and blood where he must of impacted the nails into his underneath jumping up on them as he usually does.
I went straight round to tell the neighbours and they said they only put them up a day ago to try and stop my cats going into their compost heap to poop. They were very good and did take them down straight away and offered to pay for the vet cost.
Are you on good terms with your neighbours? Even so if not, i would ask them to take the metal ones down which will cause awful injury that they would be responsible for and replace with plastic ones that can distract cats jumping on fences but wont cause harm.
Let us know how you get on