I was wondering. I assume you use that to keep the harmonics on the top string or two from making things noisy. I am doing the same thing now. Just wondering. You see, I hold the pick much like you, except that I don't curl my three fingers in. But I hold it similar with thumb and index. And I was noticing the noise, and having trouble with that. Eventually I realized that the way I held the pick kind of pulled my hand away from the bridge, making it hard to mute that string, or if I tried, I would get a scraping sound on the string with my palm, because my palm was over the string, not the bridge. If I point my index finger more down, I don't have this problem, but I really prefer to hold it as you do, with the index finger pulled back, you know the advantages so I won't go into that.
Anyway, I find using a band like you are, angle to it leave the thin strings alone, and just mutes the heavier strings a bit, allows me to do as I do and really cuts down on the superfluous noise. It really makes things cleaner. And heck, I most also mute that string anyway when I play it open. Is this your motivation using that elastic strap?
Or have I misconstrued things, and actually you had just been playing tennis, and had just stuck your wrist sweat band there so you would not lose it?
Also, great song in that lesson, I really like it, to listen to, you know, it is great music, not just a lesson.
edit: here is the lesson in question
b.t.w., figured out why your song made me think of the theme to the old British TV series "Hitchhiker's Guide to the Galaxy". Dorian scale. I also like the way your change to the minor scale there, really smooth.