What stable genius thought this up? You already have to be a citizen or permanent resident to legally purchase a gun in the US. Gun shop owners know their jobs and don’t need more regulations placed on them.
ICE should get the same notification every other law enforcement agency gets when anyone who shouldn’t be buying a gun tries to buy a gun. Should ICE get a special report? No. Should ICE get a report based on racial profiling? No Are undocumented immigrants going to line up to fill out the paperwork required to purchase a gun in a store? No. If someone wants to buy a gun regardless of immigration status they can do so without going through a background check in most every state in the Union.
Pass the Bipartisan Background Check Bill not some stand alone partisan grandstanding effort that is already included in the larger bill.