What does the 1k resistor do in this schematic?
The 1k resistor is a pull-down resistor. Not the weakest one of that, but that's okay. It is meant to pull the base of the transistor to a known state (ground) when the control signal is missing/open/high input. To prevent a floating signal or even leakage current from turning the transistor on, to make sure the strike doesn't open or engage randomly. It does form a small voltage divider, but not enough to really affect the transistor performance. Due to its value, it will waste 0.5mA to ground when the control signal is high, so it's value may need to be changed for battery applications. A 10k to 47k may be a better value.