Protecting Immigrants From Legal Exploitation Act of 2021 This bill establishes that certain acts of immigration-related fraud shall be punished by fines, imprisonment, or both. The bill provides for such punishment for a person who knowingly or recklessly executes a scheme or artifice in a matter arising under immigration law to (1) defraud any person; or (2) obtain anything of value from any person through false pretenses, representations, or promises. A person who knowingly and falsely represents that such person is an attorney or accredited representative in any matter arising under immigration law shall be subject to such punishment. The Department of Justice (DOJ) may seek civil injunctions to stop an immigration service provider from further engaging in fraudulent conduct or willfully misrepresenting the provider's authority to provide representation in immigration matters. An alien who left the United States based on erroneous advice from a person engaged in immigration practitioner fraud or the unauthorized practice of law shall not be barred from reentering the country. An alien may withdraw an application for immigration benefits that was prepared or submitted by an individual engaging in immigration practitioner fraud or the unauthorized practice of law, if the alien had no prior knowledge of the individual's fraudulent or unauthorized status. The Department of Homeland Security (DHS), the Department of State, and DOJ shall develop procedures for allowing such an alien to submit corrected filings. DHS and DOJ shall establish a program to provide grants to eligible nonprofit organizations to provide direct legal services to aliens.