The TSA checks passengers' identity and whether a passenger has a boarding pass; generally, they are not screening for immigration status.
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The coalition government committed in 2010 to reintroducing exit checks. From 8 April 2015, we will collect information on passengers leaving the UK as we do for those entering. Exit checks will provide us with vital information that confirms a person's exit from the UK.
Officials will review your required passenger travel documents (passport, visa, green card, disembarkation card (provided by a flight attendant during flight), immunization documentation, letters of confirmation or support, etc.)