~を落とす (remove / shed)

The verb 落とす ('drop') used in the [noun]を落とす frame for 'shed, remove, get rid of.' 泥を落とす ('knock off mud'), ほこりを落とす ('dust off'), 化粧を落とす ('take off makeup'), 体重を落とす ('lose weight'). The metaphor is letting something fall away.