Firstly, we haven't done screen refurbishment in over a year (mainly started around when the 5/5S/5C were out, stopped just after the 6S came out), so this might be old knowledge, however I hope it is useful.
Depending on the manufacturer of the LCD, it may or may not have a separate polariser layer, most of the time it is built into the top layer of the LCD, compared to original ones. I don't remember this causing an issue during refurbishment, since there was no polariser film to peel up, we only had to worry about not scratching the top layer of the LCD. Most of the time, this meant it was actually easier to split and clean.
After a while, we also saw a number of screens for the 5/5S/5C where the touchscreen was built into the glass, instead of the LCD, and we did start buying iPhone glass with the touchscreen built in, to allow us to refurbish these ones. Not sure if these have become more or less popular in time since I don't do iPhone repairs anymore, but just thought I would mention it in case you have come across any :)