We present measurements of the cross section for anti-neutrino charged-current quasielastic-like scattering on hydrocarbon using the medium energy (ME) NuMI wide-band neutrino beam peaking at $\sim 6$ GeV. The cross section measurements are presented as a function of the longitudinal momentum ($p_{||}$) and transverse momentum ($p_{T}$) of the final state muon. This work complements our previously reported high statistics measurement in the neutrino channel and extends the previous anti-neutrino measurement made in the low energy (LE) beam at neutrino energy($$) $\sim$ 3.5 GeV to $p_{T}$ of 2.5 GeV/c. Current theoretical models do not completely describe the data in this previously unexplored high $p_{T}$ region. The single differential cross section as a function of four momentum transfer ($Q^{2}_{QE}$) now extends to 4 GeV$^2$ with high statistics. The cross section as a function of $Q^{2}_{QE}$ shows that the tuned simulations developed by the MINERvA collaboration that agreed well with the low energy beam measurements do not agree as well with the medium energy beam measurements. Newer neutrino interaction models such as the GENIE 3 tunes are better able to simulate the high $Q^{2}_{QE}$.