Mass measurements of the nuclides 69As, 70,71Se, and 71Br, produced via fragmentation of a 124Xe 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 69As, this is the first direct mass measurement. A mass uncertainty of 22 keV was achieved with only ten events. For the nuclide 70Se, a mass uncertainty of 2.6 keV was obtained, corresponding to a relative accuracy of δm/m=4.0×10−8, with less than 500 events. The masses of the nuclides 71Se and 71Br have been measured with an uncertainty of 23 and 16 keV, respectively. Our results for the nuclides 70,71Se and 71Br are in good agreement with the 2016 Atomic Mass Evaluation, and our result for the nuclide 69As resolves the discrepancy between the previous indirect measurements. We measured also the mass of the molecule 14N15N40Ar (A=69) with a relative accuracy of δm/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 (δVpn) 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 δVpn 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 70Br, which prevents including it in the world average of Ft value for superallowed 0+→0+β 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 70Br.