Question
We have a mesquite tree that drops thousands of pods per year.  Is there a solution to stop the pods from forming and therefore dropping from the tree?

Answer
You will need to stop the flowering to keep the fruit from forming.

Florel Fruit Eliminator will reduce or eliminate undesirable fruit on many trees. Look at:
Florel?brand Growth Regulator is registered to reduce or eliminate undesirable fruit development on many ornamental trees and shrubs such as: apple, buckeye, carob, cottonwood, crabapple, elm, flowering pear, horse chestnut, maple, oak, olive, pine, sour orange, sweet gum (liquidambar) and sycamore. It also works on many other species that produce nuisance fruit.

Application must be made prior to fruit set; apply at the mid to full-bloom stage in sufficient water to wet (do not spray to run off). Good spray coverage is essential for complete fruit elimination. Apply at 1 quart per 10 gallons of water (3 oz./gallon). The amount of spray used will depend upon the size of the tree.

http://www.montereylawngarden.com/info/florel/

Spraying all the flowers will stop the fruit production for that year.