First and foremost: The best way to get any kind of technical support from Logitech for broken hardware is over the phone. Their email based support is very slow.
Second: I'm not sure why they said that they're inspecting things. I'd give them a call back with your case number, and explain the situation again: One of your keyboard's keycaps is broken, and you need them to ship you a replacement keycap.
I've had a keycap issue in the past, and they ended up sending me an entire set free of charge, no questions asked, but it did take about a week to get the order processed, and I had to contact them couple of times about it for the order to get placed.