To ask my neighbour to look after her cat?

[twoblackdogs]

My neighbour has a cat. Every morning she goes to work and lets the cat out. The cat then comes to our garden, feels at home and does whatever it wants. We can't keep the garden doors open because it wanders in and begs for food, we find dead birds in our garden, and the cat feels free to relieve itself in our flowerbeds.
The problem is we don't want a cat. And we don't want to hurt it in any way, but we don't want it in our home and garden.
The neighbour said "it's a cat, what do you want from me".
At loss what else we could do.

You need to find a way to deter it from entering your garden. Cats are generally free roaming so locking it inside all day while she works is cruel if the cat prefers being outside. Get some fence spikes, lion poo, citrus peel and a water sprinkler as a last resort. If your garden isn’t welcoming it’ll find somewhere else to spend it’s day.

YANBU and I would be taking any measures necessary to keep it out of my garden.

Second getting a sprinkler, we did that when we had a cat coming in and shitting in our veg patch. Water sprinkler to the face a couple of times quickly put paid to that. Or a super soaker.

YANBU. I like cats but I don't have one, and therefore I don't want someone else's cat causing all the hassle that a cat of my own would cause, but without the advantages of it actually being my pet.

When it comes into your garden, chase it off, squirt it with the hose, chuck something soft and harmless (like a ball of screwed-up newspaper) at it. It might be deterred if it meets with a hostile (but harmless) reaction from you whenever it ventures in.

You can get cat deterrent gel spray things and sonic cat repellers that make a noise only cats can hear, but I've never found them to work very well.

Poor cat. Neighbour needs to get a cat flap.

Water gun. I recommend:

Toy water gun

Water gun. You are too inviting to it. Scare it away when it comes in.