This bill, titled the "Honor Their Service Act," authorizes the Secretary of Veterans Affairs to establish a new grant program. Subject to appropriations, these grants will be awarded to eligible public or nonprofit private entities to provide immigration legal services. The primary beneficiaries are noncitizen veterans who are in removal proceedings, at risk of removal, or have already been removed from the United States. The funded services encompass a range of critical immigration legal assistance, including defense in removal proceedings, applications for naturalization (including through military service), and requests for parole. Grants can also support legal services for lawful reentry or repatriation for removed veterans, and assistance with upgrading discharge characterizations when it impacts immigration relief. The Secretary must establish criteria for these grants, consulting with experienced organizations, and ensure services are accessible regardless of location, including through virtual services and in rural areas.