what does "although some of them might have squeezed the concept within an inch of its life."mean?
Kelsea wasn’t the only one pleased with her library. Whenever she wandered in, she found off-duty guards lying on sofas or curled in armchairs with one of her books. Queen’s Guards had to be able to read and write, and although some of them might have squeezed the concept within an inch of its life (one day Kelsea caught Cae with his nose buried in a picture book called The Teeny-Tiny Ghost), there seemed to be something for everyone.

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What Peachey said.

Also, 'concept' here refers to this: "Queen’s Guards had to be able to read and write"

So if they almost "killed" (squeezed within an inch of its life) the concept, it means that they almost cannot read or write.

Answer

It's a nice little phrase - it basically means that some guards could barely read, but reading one or two words was "enough".

I'll break it down:

"some of them" - the guards

"might have squeezed the concept" - maybe applied their own, tenuous, idea of the ability to read and write

"within an inch of its life" - almost to death / almost to non-existence

The proof of this was the guard reading a children's book.

And to finish off with a quote by Groucho Marx, "I was going to thrash them within an inch of their lives, but I didn't have a tape measure." :D