"The only reason I can think of that she might be sent home with turquoise books might be if they match the level of phonics they are teaching right now in class, and the teacher wants to be certain that all the children understand it fully."
This is highly unlikely though, if she is being given turquoise Chip Biff & Kipper books. Those books are not matched to any phonics teaching.
DD is in Y1 as well and made huge progress in reading over the summer, so is now well ahead of the phonics teaching at school. Basically she has worked out the phonetic code (the part that hadn't been taught yet) herself, with some support by me obviously, but no direct /systematic teaching.
I didn't mind at all her being on 'blue' books at school, as these matched the current phonics teaching at school and I figured it was good for her to have that systematic teaching of the phonics she had figured out, and books to match what she had been taught that week. Despite the books being 'too easy'. But these were phonics books designed especially to practise the spellings of sounds she had been learning at school right then.
Unfortunately somebody seems to have noticed that she was finding those books easy, and she has been moved onto green and non-phonics books. She is liking them for now - the first magic key stories start here, she gets her weekly three books on a Monday and reads them all in one (fairly quick) go, she likes the adventures.
However as a parent I notice that the language is incredibly simple, and repetitive. It is WAY simpler than her blue stage phonics books were. You can really tell how the books are designed for learning words by repetition and memorising.
So she is still having books that are much 'too easy' for her, but no longer getting any benefit in terms of phonics.
My strategy is going to be to let her read those books for as long as she keeps enjoying them, because enjoyment of reading is hugely important, and I don't care what she reads or how easy it is as long as she is associating reading with fun. At the same time I will be supplementing with Dandelion Reader books. These are short (6 pages) but intense bursts of phonics, and I can match them to exactly what they are working on at school right now, plus they cover some stuff school don't. And meanwhile I will be introducing her to some other reading material, in the hope that her enjoyment of reading can mature onto stuff that I find more interesting too, not just her. I guess I won't be able to avoid the dreaded Rainbow Fairies on the way though!
OP the school might have all kinds of reasons for keeping her on turquoise, many of them not good reasons at all. Chances are they won't change their approach though . I would consider carefully what you want. You are worried about 'stretch'. But are reading books really where you want your DD to be stretched? I want reading to be something my children associate with fun, not hard or challenging. Something they enjoy. The books they read should not be chosen for maximising their learning, but for maximising their enjoyment. Stretch is important too, but not in reading books, not once you 'can read'. If you want stretch and challenge, you could let your DD do readtheory.org for 10 minutes every day or some such. (We did this with DS when he was in Y1, it is very systematic work on reading comprehension, within four months or so the little-and-often approach got his reading comprehension to the level of a 10-year-old and from then our only issue with reading has been finding large numbers of interesting/enjoyable, but yet age-appropriate books for him.)
I wouldn't have much hope for anything much from school though. Maybe what you can achieve is that they acknowledge your DD's ability, and, if you are lucky, that they don't make her read school books as long as she is reading widely at home. Maybe you could start the conversation by mentioning how a) they are not at the right level, and b) they are so boring that they are putting her off reading. And surely that is not the intention?