(To pre-empt any comments about how awful it must be to live next door to us: yes, I fully acknowledge that WE are in the wrong here. Be gentle though: life with a severely autistic child is almost breaking us.)
I would like some helpful advice about how to compensate our very awkward neighbours for what is, on paper, a minor piece of damage, but for them may have sentimental value. I'm sorry in advance for a long and rambling story!
We live next door (semis but not adjoining to these NDNs) to a couple in their fairly early retirements years, I'd guess. We've lived here nearly 16 years - they have 'always' been here and believe me, we've felt that over the years! Here's a bit of - no doubt irrelevant - background:
We are not their ideal neighbours, I'll be clear on that. For starters, we're a younger generation to them. We have children (one of whom was born soon after we moved in): they are childfree and don't seem to like children that much. We have cats, though they have litter trays and as far as I can tell, ours always poo in our garden (there's a dedicated place for them to do that) or on the 'no man's land' on the other side of the little access lane at the back of our houses. I've tried to keep things cordial re the cats, have several times suggested that if they ARE being a nuisance, that I'll buy the NDNs a powerful water pistol! or that they scare them off. We also have a messy garden. Theirs is not. However, we're far from being the only people round here who simply don't have time to garden. It's not full of junk or anything, it's more like unkempt grass and no-mow May sort of thing. And the dark and shady front yard is quite weedy. However, while they might tut about this, it's not illegal and I'm not feeling too guilty about it.
They are ... quite hard themselves to live next door to. Their shed-mounted security light is often on all night. They do a hell of a lot of very noisy DIY, with power tools a speciality at 8.30 am on weekends. They always seem to have someone over there tinkering with this or that. (That's fine, it's their right. it's not always quiet though) They bother the local council into coming and cutting back small trees and hedging on the no-man's land (trees that were bothering absolutely nobody and were a wildlife corridor) and to spray herbicide on the strip of grass and plants there - again, not an issue for anyone else. They seem not to like actual wildlife (we live at the edge of a small rural village). They're also very hung up on land access and love to remind us that they have the right of access to come onto a part of our property (at the front) at any time to trim their vine or whatever, since these all used to be council properties and there used to be no front fences (??) and there was a 'right of way' that ran across the frontages for access, and while they've had a special dispensation from the local council to buy the rights to their part of this, ours still belongs to the council and therefore they are allowed in, and technically we (and most of our neighbours!) have 'unlawful' fences across this 'route' (that goes nowhere), etc etc. I'm mentioning all this just to give an impression of the sort of barrack-room lawyer one of them can be!
His partner just seems perpetually grumpy. (She may have all sorts of personal reasons to be - I've tried and mostly failed to be friendly over the years - Christmas cards, the odd jar of jam, etc. I don't know her at all really.) It's she who tends to come over with any complaint they might have.
Ok, I know I've been prevaricating and risking the ire of MNers. Here's the current issue: DS2, who is severely autistic and has LDs, and DH, were setting out for a walk yesterday. DH was reasonably relaxed about not hanging onto DS2 on our back drive (aiming to set out across the meadow as usual) and was therefore taken by surprise when DS2 decided to bloody leg it down our drive, and into the mouth of the NDNs. This is unusual (but not totally unheard of). By the time DH had run after him and nabbed him, DS2 had for some reason, pried off the decorative house number tiles on a sort of home-made wooden stand at the mouth of their drive. The tiles had come off extremely fast (the adhesive looked knackered and ancient) - two of them I think have broken as they fell off. 
Obviously I'm really upset for NDNs about this. Regardless of what a PITA they have been over the years (and I know we're not their favourite people) this was their property and they valued it, and it's horrible to have something of yours broken, even if by accident or through no malicious intent. DH had hustled DS away on their walk (I was volunteering at a village event so not at home) and the NDNs were out for the day, but he rang me, and I, horrified, immediately whatsapp'd the NDNs and 'fessed up. I said I was very sorry, and that they should please tell me what we can do to make it up to them by means of repair or replacement.
I didn't get a reply though I can see they've read it. Later on, DH was supervising DS in our garden for a bit and the lovely NDN who tends to be the less friendly of the pair came out of her drive and snarled at DH that she 'supposed he'd be paying for a return trip to the Canary Isles, would he, since that is where the tiles were bought and they have sentimental value' ... DH said, he was very sorry.
NDNs do know our son is severely autistic. They have shown zero compassion for either him or for us over the years, we and he are just an annoyance.* Of course, why should they care if he's got a lifelong disability which occasionally makes him behave like this? It's nothing to them and it's not THEIR fault. It's not his, or our fault, either, but clearly he got out of our control and that's on us.
But I can see that they will be ramping this up into a grudge. I would go a long way to avoid this becoming a major problem. (they have form for blowing up minor irritations with their neighbours on their other side, who have now moved away, and in fact this led to those neighbours having two house sales fall through! Long story) I'm terrified that they'll simmer about this and it'll all blow up in our face, or they'll make it a 'dispute' that would have to be declared to an estate agent.
So how do I compensate them? I've already sourced the tiles online and I can, for about £50 all in, have some shipped here to replace them in the same style. (Tiles themselves cost about £7 each but shipping ...) That, coupled with a 'I'm very sorry' card signed by DS if I can get him to, and a bottle of wine? I mean no, I'm not about to fund a return trip to the Canaries but she can't have been serious, surely?? I just want to try and do the right thing here, but if I'm honest, I also want to try and get the moral ground too, I want to be seen to have done all that's reasonable so that we know at least that we did all we could. Because I have a nasty feeling this may run and run...
*(Once, DS2 managed to break through our not inconsiderable defences and exited the house and ran into the village. We immediately called the police as we were pursuing him a few minutes behind. The police turned up at our address while we were cornering him in the village. The NDNs went round to our house and BULLIED my lovely older son, telling him it was a disgrace that the police were waiting outside (to be clear, my lovely and then 15 yo son asked them in, on my instructions as we were on our way back with DS2, and they politely refused as he was under age). They said some really unpleasant things to DS1 about us and our younger son. This all seemed off the back of us relaxing our vigilance for five minutes. We have to be hyper-vigilant and locked-down ALL the time. We're exhausted and sometimes - as with all parents of SEND kids at one point or another - the defences break down and my son will take advantage of that. We're just so tired. There's no bloody respite available from our county, they won't even allocate us a SEN social worker because they're like gold dust, and our relationship and physical health is suffering. None of this is of any interest to our NDNs of course, but it's breaking us. This sort of thing feels like the last straw.)