It isn't hungry enough to eat the whole serving. Reduce serving sizes rather than encouraging it to clean its plate and become overweight. Some cats have digestive systems which only accept small amounts of food at a time. Height of foodbowl. This is an odd one for most people.
Some cats have problems eating from a bowl on the floor.
Older cats and those with joint trouble have problems crouching down to eat their food. Hunting and scavenging. Indoor-outdoor cats have the opportunity to hunt and scavenge. To avoid hurting any feelings, you could tell neighbours that it is on a medical diet and treats could harm or even kill it. Your neighbour might be getting great pleasure from feeding the cat so another solution is to give the neighbour a small container of its 'permitted food' and a allow her to feed it a handful of this each day, but explain that other types of food will lead to high vet bills.