After 26 yr in outburst, the black hole X-ray binary GRS 1915+105 dimmed considerably in early 2018; its flux dropped sharply in mid-2019, and it has remained faint ever since. This faint period, the "obscured state," is punctuated by occasional X-ray flares, many of which have been observed by NICER as part of our regular monitoring program. Here we present detailed time-resolved spectroscopy of one bright flare, whose spectrum shows evidence of high column density partial covering absorption and extremely deep absorption lines (equivalent widths over 100 eV in some cases). We study the time-dependent ionization of the obscuring gas with xstar, ultimately attributing the absorption to a radially stratified absorber of density ∼10^(12)–10^(13) per cu.cm at ∼few ×10^(11) cm from the black hole. We argue that a vertically extended outer disk could explain this obscuration. We discuss several scenarios to explain the obscured state, including massive outflows, an increase in the mass accretion rate, and changes in the outer disk that herald the approach of quiescence, but none are entirely satisfactory. Alternative explanations, such as obscuration by the accretion stream impact point, may be testable with current or future data.