How far Jupiter's cloud-level zonal winds penetrate into its interior, a question related to the origin of the winds, has long been a major puzzle about Jupiter. There exist two different views: the shallow scenario in which the cloud-level winds are confined within the thin weather layer at cloud top and the deep scenario in which the cloud-level winds manifest thermal convection in the deep interior. We interpret, using two different models corresponding to the two scenarios, the high-precision measurements of Jupiter's equatorially antisymmetric gravitational field by the Juno spacecraft. We demonstrate, based on the thermal-gravitational wind equation, that both the shallow and deep cloud-level winds models are capable of explaining the measured odd gravitational coefficients within the measured uncertainties, reflecting the nonunique nature of the gravity inverse problem. We conclude that the high-precision Juno gravity measurements cannot provide an answer to the long-standing question about the origin of Jupiter's cloud-level zonal winds.