Always put the head, tail, guts, out in the back garden on top of the 3' high compost heap. Corvids immediately take their pick and overnight the remains disappear. Never anything left the next day.
An oldish cat was discovered by our terrier in a corner of the garage. Its owners had put round a leaflet crying out for news of their beloved missing moggie. We rang them, they happily collected their cat and later gave us a bottle of Chablis!
I suspect my fish remains seduced the cat in the first place and it was sleeping off the feast.
Try putting your fish remains in the back garden - it might work for you too!
Trish