Q.When should dried pea pods be removed from mimosa trees?
Do I let them fall or trim them off?

Certified GKH Gardening Expert
There is no reason to remove the seed pods from the mimosa trees except aesthetics or to prevent unwanted reseeding. If you don't like the look or the litter, go ahead and trim them off if you can reach them. If you let them fully mature and fall to the ground, you can sweep, rake or pick them up if needed. The second article discusses the problems of reseeding.
https://www.gardeningknowhow.com/ornamental/trees/mimosa/growing-silk-trees.htm
https://www.gardeningknowhow.com/ornamental/trees/mimosa/mimosa-tree-weeds.htm