Ohm's Law. 24 volts through 300 ohms gets you 0.08 amps and 1.92 watts. I'm not sure of the circuit diagram, though. I haven't had a reason to mess with it.
IF that 300 ohms is
in series with 300 ohms presented by the voltmeter (which is easy to believe), then you are okay at a half watt. You'll be dissipating .48 watts in that case.
Still, that's running pretty close to the edge, and a larger wattage would be more robust. Toss a 5 watt in there and it will probably never burn out again. As long as it's 300 ohms, you could run a 100 watt resistor in there, and it would work just fine. Probably wouldn't fit, though!