There's a sexy-eye wink right after they shake hands. Of course, the door is locked, Ten isn't Four who kept the Tardis doors open when not inside. However, then there was a bit less of concern to worry about anything happening to the TARDIS that Gallifrey or Logopolis both of which could repair the TARDIS - both of which are now gone.

Ten meanwhile stands there silently watching the both of them. No. No. No She didn't just pick up on the properties of the TARDIS key in his inside his infinite suitcoat pocket.

"Sounds like you have some wires crossed in your device."