You don't need to fertilize dead grass, but continue to fertilize all the rest of it to encourage spreading back to fill the dead spots. Water the entire yard to encourage any growth from the dead areas. If the roots are still alive, it may recover. If it seems to be recovering, then fertilize at half the normal monthly rate until you are mowing it. Then resume normal strength monthly applications.

For others who find caterpillars eating their lawn, there is an organic alternative to whatever the lawn company sprayed. What they sprayed will likely kill the birds that ate the poisoned caterpillars. The organic alternative is a bacteria which causes paralysis in caterpillars. It goes by the name BT. You can find it in one form or another everywhere. Spray it on and it affects the caterpillars instantly so they stop feeding. BT is only a disease in caterpillars, not birds, mammals, fish, toads, or lizards.