Question
Is there a way to prevent a mesquite from having pods

Answer
An option is to use a growth regulator such as Florel? Florel?is the brainchild of Monterey and inhibits the production of fruit when applied during the blooming stage. The active ingredient, Ethephon, is non-toxic and converts quickly to ethylene when it comes in contact with plant material.

However, if using chemicals in the garden concerns you then there are only two other options available. The first is removing the flowers by hand which on a small tree may be a good alternative but once the tree increases in size becomes a tad untenable. OR remove the tree.

Here is a web link to this product. http://www.montereylawngarden.com/info/florel/