Neighbour trimmed the tree that hangs over in to her garden......but

[Blushingm]

She chucked all the bits she trimmed over in to my garden

Is this normal?

I don't mind her trimming it - trees grow - but I'm pissed off that she threw it all over in to my garden

Don't make this the hill you die on. Start trimming the tree regularly. Sorted.

No, she has to offer them back to you, which you can decline.