I hold the strops, leather/linen, separately the way I saw most barbers do in my youth. As a kid I was always fascinated by watching barbers strop and watched attentively. I also got instruction from a couple of them as an adult back in the '80s when I knew a few socially. OTOH, I don't think there is a right way or wrong way when it comes to holding one or both. As long as the strop is taut and does the job.