Final answer:
Clara Barton demonstrated her international influence by assisting with military hospitals in Europe in 1869 and petitioning for the establishment of an American branch of the International Red Cross in 1881.
Step-by-step explanation:
The information indicating that Clara Barton had international influence is her involvement in international affairs through the Red Cross. In 1869, Barton's work extended beyond American borders when she traveled to Europe to assist with military hospital preparation and provide aid to the poor. This demonstrates her global impact since it involved working in different countries and alongside international organizations.
Moreover, her initiative in 1881 to petition President Chester A. Arthur to open an American branch of the International Red Cross Organization also reflects her international reach, as she sought to establish a connection between American humanitarian efforts and the broader, global Red Cross movement, which spanned various nations.