When marking an animal for the mark/recapture technique, what can a scientist do to ensure the mark does not lower the organism's chance of survival, and thus throw off the population estimate?

You should make it unobtrusive to avoid it attracting attention or hindering it in any way. What you can do is shave a small patch of fur from underneath the animal, and this couldn't be noticed by predators from sides but could easily be noticed by a scientist that captures it.