Such supplications to the one-tusked Lord are given unconditionally, with full trust that He will do what is best for us, though not necessarily what "WE" might think is best. We do not demand of the Lord; for He, like a parent, provides not as we desire, but as we truly need. Prayers of supplication may come forth in the natural language of our hearts.
Leaving a problem at His holy feet means we let it be there and do not carry it home with us. Nor do we worry or wonder about how it will be handled, when it will be taken care of, or if it will be taken care of at all. In full unquenchable faith we leave the matter there, at the feet of the God, and walk away from the temple or the shrine, feeling that release has started and solution will be forthcoming. We must have this kind of faith for religion to work within us.
To carry home with us the same problems, fears, and worries would be to take back the offering we have given the Diety to dissolve. This is like the rich and famous who buy with gifts and do not give at all, slyly expecting more than something in exchange, gaining "papa" rather than "punya" and not knowing the difference. The course of events later show how He works for our ultimate spiritual welfare,
"from "Loving Ganesa"