Short answer, they will never know if it is an insurance replacement vs. warranty replacement. When you send it in under an insurance claim (like Asurian), it goes to a mass receiving facility that isn't even Asurian, just a middle man that gets the phones, removes batteries, micro sd cards, etc. and they all go in their seperate boxes then then phone goes somewhere for reconditioning or trash.
I found this out the hard way by shipping one back with the micro sd card still in it. Tried to get sd card back, but no go as they don't even have a way to track phone once it hits receiving facility. They record the MEID or ESN to credit sender, but other than that it is on the disassembly line never to be found again. Somewhere there is a bunch of batteries and sd cards floating around lol. I hope they enjoyed my pics, there was some GOOD ones in there lol.