I wanted to say plug it up so you don't waste metered water.
The pitfall I saw was if you have a backflow preventer on the feed from the water main and no expansion tank for your water heater. This combination could lead to unusual pressure buildup in your system where a pressure relief valve would be needed.
Does twisting the plastic dial stop the trickle? If so adjust the dial to just at the point where the trickle stops.
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On the ones I've seen like that . It's not actually a knob that you can adjust.. It's more like a cap.. The relief in the valve is per set at the factory... Might be worth a shot to try.. I don't think I would force it to turn with water turned on incase it were to snap off
Are you sure it's a pressure relief valve? It could be an auto trap primer. Everytime water is used it trickles water to keep the trap filled. Prehaps that sink wasn't used very often at one time and the trap was drying up.