The target circuit board is powered via a 9v battery, though Vcc for the ATtiny44 is +5v. The only other noteable part of the board would be the 3055L MOFET which I'm guessing is used to drive the Solenoid.
I would guess that the main draw is the solenoid, so as long as the trigger (which activates the Solenoid) is never fired, I'm pretty sure the draw is under 350mA.