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Globular clusters (GCs) play an important role in the formation and evolution of the Milky Way. New candidates are continuously found, particularly in the high-extinction low-latitude regions of the bulge, although their existence and properties have yet to be verified. In order to investigate the new GC candidates, we performed high-resolution NIR spectroscopy of stars toward the bulge using the IGRINS instrument at the Gemini-South telescope. We selected 15 and 10 stars near Camargo 1103 and 1106, respectively, which have recently been reported as metal-poor GC candidates in the bulge. In contrast to the classical approaches used in optical spectroscopy, we determined stellar parameters from a combination of line-depth ratios and the equivalent width of a CO line. The stellar parameters of the stars follow the common trends of nearby APOGEE stars in a similar magnitude range. We also determined the abundances of Fe, Na, Mg, Al, Si, S, K, Ca, Ti, Cr, Ni, and Ce through spectrum synthesis. There is no clear evidence of a grouping in RV-[Fe/H] space that would indicate the characterization of either object as metal-poor GCs. This result emphasizes the necessity of follow-up spectroscopy for new GC candidates toward the bulge, although we cannot completely rule out a low probability that we only observed nonmember stars. We also note discrepancies between the abundances of Al, Ca, and Ti when derived from the H- vs. the K-band spectra. Although the cause of this discrepancy is not clear, the effects of atmosphere parameters or NLTE are discussed. Our approach and results demonstrate that IGRINS spectroscopy is a useful tool for studying the chemical properties of stars toward the Galactic bulge with a statistical uncertainty in [Fe/H] of 0.03 dex, while the systematic error through uncertainties of atmospheric parameter is slightly larger than in measurements from optical spectroscopy.