Today I saw the tell-tale swept-earth mark of one of those troublesome brush turkeys. Turkeys are driven by their instinct and no amount of swearing and arm-waving will stop a male from building if there is material available and a sheltered spot for the heap.
The only real deterrent is wire mesh pegged down over the mulch or large branches or rocks laid on top. It does look ugly, but if the turkey can't scratch it can't collect mound material. Note that a turkey is totally single-minded and strong in the legs, and don't be surprised if he rakes quite heavy lumps aside in order to collect material. He has nothing else to do all day!
That leads to the second possible deterrent method, which relies on other instincts. You can persuade a turkey that he has a rival for his territory by installing a suitable mirror near his mound. He will then spend all his time trying to drive off the intruder, rather than raking your garden. It may be worth a try!
Once a suitable volume of mulch has been collected, the turkey's mound begins to break down, generating warmth to incubate the eggs. Unlike gardeners, turkeys seem to have no problem getting that hot composting process up and running.
We gardeners can learn a lot from the turkeys. To start with, collect sticks as well as leaves, so that air can filter into the heap. Shred, as with your turkey claws, all of the softer materials. Make sure you collect mostly moist material, and, finally, pile it up high and turn it over regularly. You too can make a hot heap!
Note that the turkey's original mound material can't heat up again, so feel free to keep an eye on the pile and retrieve your mulch once the young have hatched.