Yes! I totally did that and it helped. But you know what helped instantly? I put some moisturizer on my wrist, and that did an instant fix...but yeah, tightening the strap also worked.
But what is weird, and I mentioned this...is the heart rate monitor works just fine. I had a Fitbit a couple years back, and at least Fitbit had the foresight, and the decency to let their customers know (I think it was in the manual) that dark tattoos would affect the performance.
It's kinda annoying, all of this still. I really hope, and I assume there will be some sort of a firmware/software fix for this.