Jessie, To "tamp" or "tamp down" means to press something down by hitting it. -She tamped down the soil around the rose bushes. -With his finger he tamped the tobacco in his pipe. Figuratively "tamp down" means to "reduce, subdue, hold in check -Nobody wants to see Jon's talent, or anybody's be tamped down to mediocrity. -The struggling Royal Bank of Scotland is trying to tamp down the latest rumors that it will sell its US subsidiary. -Obama certainly tamped down the black vote with his support for gay marriage. -We ought to tamp down our enthusiasm for spending money that does not exist.

To "tamp" or "tamp down" is to compress or pack something down, like gunpowder in a muzzle-loading rifle, using a series of taps or strokes. In this context, the speaker is using the expression to mean reducing something.