Migrant Processing and Protection Act of 2023 This bill expands the category of non-U.S. nationals ( aliens under federal law) who are subject to expedited removal (i.e., removal without further hearing or review) and addresses related issues. Specifically, this bill requires expedited removal for individuals who are unlawfully present or who unlawfully entered the United States. (Currently, DHS may, but is not required to, apply expedited removal to unlawfully present individuals who have been physically present in the United States for less than two years.) This section also requires detention for individuals who (1) are subject to expedited removal, (2) are subject to expedited removal and have expressed an intention to apply for asylum, or (3) have established a credible fear of persecution and are awaiting consideration of an asylum application. If DHS cannot comply with this detention requirement or remove an individual to a safe third country, DHS must return the individual to the neighboring country that the individual traveled through to reach the United States while the individual's case is pending.