Q: What is best, pushing the burlap down in the hole or totally removing the burlap around “balled and burlapped” tree rootballs?

A: It’s best to remove to totally remove it. Burlap is often chemically treated to prevent it from rotting too soon at a nursery. Although it eventually deteriorates in the ground, it inhibits root growth. The best technique is to put the tree in its final position then excavate far enough around the root ball so you can cut away all of the burlap you possibly can. The same goes for wire caging, if present. You may need a hacksaw or bolt cutters to clip the thick wire but research has shown that wire cages can damage roots as the grow through.

See Do I Remove Root Balls?