Hello: The relief valve is the third line of defense in preventing a water heater from exploding. First is the thermostat, which should maintain temperature. Next is the high limit, built into the control. It should shut the gas off if water gets too hot. Finally is the relief valve. Tuning the control off regularly, seems to me, not to help. Controls aren’t designed for daily operation.
As you don’t know where the discharge leads, the relief valve should simply be replaced. That way you should not need to worry for years. I’ll add that modern controls seem to work quite well in doing their job, but should debris get into the valve itself, it could prevent the valve from shutting off. That’s why most plumbers (and many inspectors ask for) add a “dirt leg” to the gas line for junk in the line to fall into, before getting to the valve.
From Watts, who makes T&P valves, “Following installation, the valve lever MUST be operated AT LEAST ONCE A YEAR to ensure that waterways are clear.” Here is the link: http://media.wattswater.com/PG-TP-ASME.pdf That’s something to share with your landlord. 😉