No, the form doesn't impact your refund. In fact, the form 1095-C  is not reported on your tax return. The form is a receipt from private insurers or employers confirming you had health coverage. Keep it for your records.

When going through the Health Insurance section, all you had to do is indicate that you have health insurance coverage all year (if applicable) and that you were not enrolled in other plans (such us Obamacare of Healthcare.gov plan).

If you did so, no changes are needed for your tax return.