Mass measurements of the nuclides As69,Se70,71, and Br71, produced via fragmentation of a Xe124 primary beam at the Fragment Separator (FRS) at GSI, have been performed with the multiple-reflection time-of-flight mass spectrometer (MR-TOF-MS) of the FRS Ion Catcher with an unprecedented mass resolving power of almost 1000000. Such high resolving power is the only way to achieve accurate results and resolve overlapping peaks of short-lived exotic nuclei, whose total number of accumulated events is always limited. For the nuclide As69, this is the first direct mass measurement. A mass uncertainty of 22 keV was achieved with only ten events. For the nuclide Se70, a mass uncertainty of 2.6 keV was obtained, corresponding to a relative accuracy of dm/m=4.0×10-8, with less than 500 events. The masses of the nuclides Se71 and Br71 have been measured with an uncertainty of 23 and 16 keV, respectively. Our results for the nuclides Se70,71 and Br71 are in good agreement with the 2016 Atomic Mass Evaluation, and our result for the nuclide As69 resolves the discrepancy between the previous indirect measurements. We measured also the mass of the molecule N14N15Ar40 (A=69) with a relative accuracy of dm/m=1.7×10-8, the highest yet achieved with an MR-TOF-MS. Our results show that the measured restrengthening of the proton-neutron interaction (dVpn) for odd-odd nuclei along the N=Z line above Z=29 (recently extended to Z=37) is hardly evident at the N-Z=2 line, and not evident at the N-Z=4 line. Nevertheless, detailed structure of dVpn along the N-Z=2 and N-Z=4 lines, confirmed by our mass measurements, may provide a hint regarding the ongoing ˜500 keV discrepancy in the mass value of the nuclide Br70, which prevents including it in the world average of Ft value for superallowed 0+?0+ ß decays. The reported work sets the stage for mass measurements with the FRS Ion Catcher of nuclei at and beyond the N=Z line in the same region of the nuclear chart, including the nuclide Br70.