Baby gate screws protrude too much

We have a baby gate that didn’t stand up to the rigor of our toddler, so I had to upgrade the drywall anchors. The problem is that the screws for the new drywall protrude too much for the gate to snap into the button the top. Any ideas of how to shrink the top of the screw (or somewhere else) to give enough room for the button to snap in?