H.Amdt.797 - Amendment modifies sections 3006, 3007, and 3032 of the bill. It modifies section 3006 by allowing any alien who is subject to expedited removal to ask for asylum; modifies section 3007 to provide that aliens suspected of being terrorists by their home governments can receive asylum only if they can show that a central reason for the actions taken against them was animus on account of race, social group, sex, or political opinion; replaces section 3032 by substituting language providing that aliens who are barred from restriction on removal and who are ordered removed can be detained pending removal, in the Secretary of Homeland Security's nonreviewable discretion. The replacement language also requires the Secretary of State to ensure the protection of an alien barred from restriction on removal, who has been ordered removed but otherwise given protection under the immigration law, prior to that alien's removal.