To repair any vehicle quickly, just use Guerrilla Express while inside your vehicle. The vehicle can now be found in or near the camp you traveled to, with no damage.

If you hijack an EDF tank, you are unable to heal it by teleporting to a safehouse. In fact, the tank disappears. You are however able to heal tanks or any other vehicles by going to a demolitions master. Leave the area during the event and you will fail. After the challenge ends you should have a full health EDF tank where you left it before the challenge.

Exit a vehicle near the end of a mission. Complete the mission and return to the vehicle. It will be fully repaired.