not sure what to do with cat fighting situation

[Schooldramabannana]

We've lived here 5 years and had an ongoing problem ever since we got our cat 2 years ago
He loves to be outside although does come in every evening to sleep
We have a next door neighbour with 2 cats, one male and one female who generally stay outside even at night unless very cold.
They generally sit on her shed.
Our cat will go into their garden and then a cat fight breaks out.
Neighbour has made it clear she feels we are responsible and as he's aggressive and goes into their garden so her cats territory it is his fault and sent us the bill after the first fight they had.
I knocked and explained I wouldn't be paying a bill for a cat fight, that mine too gets injuries from being outside and I can't expect people to pay for that as they are wild animals really.
She wasn't happy and hasn't spoken to us since but we don't see her much anyway so no massive issue!
I've just heard a cat fight so looked out the window and there he is in their garden fighting with her male cat, she comes out and throws a jug of water over them and gets her cats in calling ours a ginger cunt as she is doing it
What am I meant to do?
I don't get why he still goes into the bloody garden; he

Oh, and I can't say I blame people who take extreme measures to protect their pets in the face of the fecklessness of so many cat owners.

No need to be so aggressive WT, I respect your opinion on this and do share some of it. I dunno, I just thought a thread about a hypothetical (to us) cat with the op asking for advice doesn't deserve such anger. That's my opinion, in a sea of others that make up mn threads, and you are as free to ignore it as I am to state it.

It must be very difficult on a housing estate with small gardens.. We have 16 acres and ours still occasionally gets into scraps. He's another ginge too. When we first got him he was regularly beaten up by next door's cat, now that died he rules the area.

Could you speak to her about paying towards cat proofing her garden? So he can't get in. Or offer to try and do shifts so they're out at different times? I'd be upset if my cat was regularly getting hurt too, so while I don't think the cat should be locked in, it would be nice of you to offer a bit of help..

We aren't allowed to cat proof
She's out all day and won't have hers in at night so I feel I've been fair making sure mine is

Why doesn't she keep her cat in at night?

Is SHE not allowed to cat proof either? I meant do hers because you're not allowed..

She won't clean the litter tray so won't have the cats staying in at night time / any long periods of time
Even hen she goes away she pays someone just to come and feed but they are still outside not inside
No the rules of this development estate means she wouldn't be able to cat proof either as we aren't allowed to modify at all

My cat now "fights" but he's more noise than action.

My previous white cat (male) was friendly but got attacked needing drains etc for wounds. No way I'd approach owners about it, it happens.