Answer: You are describing evidence of sod webworms. The moths lay their eggs on the blades of the grass and the larvae feed on the turf. You can control them with the bacterium Bacillus thuringiensis (Bt) which is registered for use against all three species and is most effective in controlling young larvae. Some commercial products include Dipel, Green Light Bt Worm Killer, Safer Caterpillar Killer, and Thuricide. Be sure to apply to the lawn as directed on the product label. For more in-depth information about sod webworms in Florida, here's a publication from the University of Florida: http://edis.ifas.ufl.edu/IN608.
Best wishes with your lawn!
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