How to efficiently remove the food particles stuck in the scrubbing pad?
I put the hot water tap on an extremely slow trickle to wet the pad.
Then squeeze dishwasher detergent + baking soda to work up a sud on the pad.
Then squeeze and "massage" the pad as best you could under the slow hot trickle.

My actual motivation has always been remove the stale stink from the pad. Somehow, the side effects are that the food particles are also dislodged from the pad by the suds.

This must be due to surface tension mitigation and anti-static effects of the suds (disengaging the attraction of food particles from the pad bristles) plus the washing action of the slow hot trickle. If the water is too hot, you might have to put on kitchen gloves.