Unlocking an iPhone modifies the device so it can be used with any SIM card. If inserting a SIM card into the device produces an "Insert SIM card with no PIN lock" error, the unlock was performed incorrectly. Within the U.S., attempting to unlock an iPhone voids its warranty and violates the Terms of Service agreement with AT&T. Re-insert the AT&T SIM into the iPhone if you don't want to void its warranty or your AT&T agreement.
Disconnect the iPhone from iTunes. Push the end of a paperclip into the hole next to the iPhone's SIM tray and push it in.
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Remove the SIM tray from the iPhone. Push out the third-party SIM card and set it aside for later use.
Insert an AT&T SIM card face-down. Replace the SIM card and press it back in. Wait for AT&T's name to re-appear in the upper left corner of the screen.