Remembering Our Local Heroes Act This bill directs the Department of the Interior to establish a grant program to fund construction, restoration, renovation, and maintenance for memorials designed to perpetuate in a permanent manner the memory of individuals or groups, living or deceased, who are veterans of the Armed Forces who served on or after April 6, 1917; are members of the Armed Forces killed while on active duty as a result of injuries incurred in the line of duty on or after April 6, 1917; have served as law enforcement officers; or have served as firefighters. No grant awarded under the program may exceed $100,000.