I’d paint the top part pink, using loads of paint so it drips down in between the slats of their side 
Honestly, with a bit of clever planting and/or trellis you can make it look ok. But if it’s cutting out the light from your garden then they need to rethink it.
Could you invite them round for a bbq or something?! At least then they can see how awful it looks for themselves.
I think painting it a light colour would help the light issue a bit, but depending which side the sun shines from it could end up making your garden unusable if there’s no sunshine at all, which is not fair. They need to know how it’s affected you even if you tell them in a really polite and nice way.
My garden also looks a bit like a prison yard. Last year I started a mural which has really helped brighten it up - excuse dodgy selfie, it’s the only photo I have of it! (Never quite finished!) It’s still on my to do list. If you fancy a mural to disguise it a bit give me a shout 