I am not in Texas but S.E. WI. I guess it depends somewhat on the pear variety. I grow Summercrisp which is picked and eaten at the green/ripe stage while still crispy (mid-late August). My Bartlett pears are picked usually around Sept 11th while firm but just starting to turn from dark green to a light green/yellow.

Most European pears are best picked before fully ripe and allowed to ripen off the tree. If left to fully ripen on the tree they often are black around the core. The tricky part is when to pick. Too late and they are rotten around the core. Too early and the pear ripens but without flavor or sweetness. I try and judge them by the skin color and pick when just turning to light green/yellow but the fruit is still very firm.

I hope this helps! Put a sign by your pears stating "Do not eat, sprayed with pesticide". Perhaps that will deter the neighbors.