Take it easy
The mice damage typically happens during the winter time when the groud is covered by the snow and the mice can hardly find anything else to eat. It is spring now, happy time for the mice too, so the situation won't worsen. Just spread some lawn seeds to the damaged areas. The lawn will recover.
The same thing may happen to you again next year, if your lawn is still relatively new, because the root of the lawn is still soft and attractive to the mice. After the root gets tough and tight in 3 or 4 years, the mice can no longer chew it. Then you will not have the headache anymore.