Jamieson, Fausset and Brown on Exodus 33:5

5. put off thy ornaments--In seasons of mourning, it is customary with Eastern people to lay aside all gewgaws and divest themselves of their jewels, their gold, and every thing rich and splendid in their dress. This token of their sorrow the Lord required of His offending people.

that I may know what to do unto thee--The language is accommodated to the feeble apprehensions of men. God judges the state of the heart by the tenor of the conduct. In the case of the Israelites, He cherished a design of mercy; and the moment He discerned the first symptoms of contrition, by their stripping off their ornaments, as penitents conscious of their error and sincerely sorrowful, this fact added its weight to the fervency of Moses' prayers, and gave them prevalence with God in behalf of the people.