I think this depends on just how much you want to take. I would recommend taking small portions, including a small amount of soil with the mulch, and treat it very carefully. Put it in your own mulch, if you have any. If you don't have any, you can mix the small amount of the soil into the
root zone of your pioneer plants. Also, if you have any of your own
compost, I would put that just above the soil you incorporated. Then put the mulch you borrowed on top of that. Then, put some herbage cut from your own property on top of that mulch. In this way, you may be able to inoculate your degraded soil with the microorganisms from the healthier bit of ground. You will also be mimicking a natural soil horizon development that feeds from the top down.
It could look something like this:
Top
fresh chopped herbage
mulch from healthy site
your own compost if you have any
top, organic soil layer with healthy soil gently snuggled in (not broken into too many pieces which will further harm any fungi)
your own soil
Bottom
As to the amount to take, only you can judge.
If you are able to spare anything in the near future, you can also bring some herbage/mulch material/compost back to the land that you are taking mulch from. You could also think about arranging any branches and logs into "catch logs" across the contour to help retain any leaves that fall, without really damaging the site and doing that much work.