Quail saved Earth from an alien invasion by making a deal with the aliens, where they agreed to spare Earth because Quail impressed them with his bravery

due to advanced technology that allows them to monitor his thoughts and ensure he isn't hiding any dangerous information

McClane advises Quail to accept the situation and return home never telling anyone about the trip

because it is deeply embedded and tied to his sense of identity. Removing it might cause psychological damage or be technically impossible.

because his mission involved classified operations that could compromise security or reveal sensitive information; he killed a person there

"Well, I offer the suggestion that you better not kill him. If you do they'll return."

Quail's first thought upon waking is about his desire to go to Mars. He longs for a more adventurous and exciting life than his mundane job can offer

they could implant another set of memories to cover up his Martian mission. He communicates with the Interplan agents through his thoughts

a box of Martian souvenirs, which confuses him because it suggests his memories of being on Mars might be real, conflicting with his beliefs that he hadn't been

Quail talks about Mars because he can remember actually being there, despite thinking he never went. He remembers a mission where he was a secret agent

"In fact," McClane said, "it's touching." "But arrogant," the police official said... "Inasmuch as when he dies the invasion will resume."

The objects in the packets are imitations, meant to serve as props to support the implanted memories and make them feel real.