Permanent residents do not "apply" for reentry. They just need to show their green card and ID upon arriving in the U.S. Likewise, the EO did not merely delay visa applications. It denied entry, without any process, to people whose applications had already been approved and who had already received visas.

If the EO had merely delayed applications for three months pending additional procedures, courts across the country wouldn't be granting TROs to stop enforcement of it.