The undamaged tile looks exactly the same as its normal counterpart, while the damaged tile has a faint, yellow glow originating from inside it. This special tile variant may spawn already damaged at the start of a mission.
Destroying the tile will reveal a "strange object" hidden inside it; upon being picked up it will broadcast a signal. After the end of that turn, a Strange Pod will fall from the sky, similarly to a Time Pod. Protecting or rescuing the Pod will unlock one of three special Pilots and grant the Distant Friends achievement.
Keep in mind that the "strange object" must be picked up by a Mech, simply protecting it until the end of the battle won't summon the Pod.
It seems like the marked tiles never appear on the first visited Island, nor do they appear during Boss battles.
They also haven't been found in missions where a Time Pod appears.
The special pilots are a reference to Subset Games's earlier title, FTL: Faster than Light.
The sound that plays during the signal broadcast is the same as the FTL jump drive.
The Pod resembles a broken section of the Federation cruiser from Faster than Light.