I would just nip that errant piece of leather off with a scissors.
The rough out Muleskinner leather is a lot different than most other shoe leather, as far as conditioning goes there are fewer options. I certainly would not use mink oil on them. I don't own a pair of the rough outs and I don't think I would, but if it were me I would probably use the Red Wing suede brush to spot fix and clean. And a regular shoe brush for general duty and daily cleaning and inspection. I would also consider a light spray of some sort of leather protector/water proofing, Kiwi, Red Wing or otherwise. Very light spritzing, definitely would not soak it in.
But the best advice would be to wear the heck out of them. I think the Muleskinners are supposed to look pretty rough, as part of the appeal.