Under the education law incidents of corporal punishment are required to be reported about any teacher, but this does not mean a district is required to analyze and interpret the meaning of a jury verdict about an incident that occurred 12 years ago. In fact, without knowing more than that there was a verdict for battery, it means nothing reltive to corporal punishment.
The proper thing for the teacher to do is to write a letter to the licensing division of the department of education and explain the circumstances, because if it is arguably relevant, not informing them may be worse then informing them.
As to remedies against the district for reporting the verdict, it really depends upon the facts, and what the person making the report knows.