No clue on the longevity, esp. for a daily use item like a wallet. They tend to be high wear in my experience.
EDIT: oops. Posted 2 methods of xfer, rather than the second example I MEANT to post: You can also try feeding your jute directly through an ink jet, if it is “free” (it sounds as though yours is already a part of the wallet, so it wouldn’t work this time, but maybe if you make another… Here’s one of those tutorials.
Also, while I’m here, another method which I don’t think will work for your case, where the wallet’s already made, but for future reference, is screen printing.
Finally, my first thought, which I left off originally, is that you’ll really want to just dye it by hand, maybe with a stencil. You could laser cut the stencil…
here’s an idea - the poor man’s Batique would be covering the negative space with a paper template and then possibly using tool dip or water proofing spray paint to do the label in some durable way