UTe2 is a recently discovered promising candidate for a spin-triplet superconductor. In contrast to conventional spin-singlet superconductivity, spin-triplet superconductivity possesses spin and angular momentum degrees of freedom. To detect these degrees of freedom and obtain the solid evidence of spin-triplet superconductivity in UTe2, we have performed Te-125-NMR measurements, which are sensitive to the local spin susceptibility at a nuclear site. We previously reported that the shoulder signal appears in NMR spectra below the superconducting (SC) transition temperature T-c in H parallel to b, and a slight decrease in the Knight shift along the b and c axes (K-b and K-c, respectively) below T-c at a low magnetic field H. Although the decrease in K-c vanished above 5.5 T, the decrease in K-b was independent of H up to 6.5 T. To clarify the origin of the shoulder signal and the trace of the decrease in K-b, we compared the Te-125-NMR spectra obtained when H parallel to b and H parallel to c and measured the Te-125-NMR spectra for H parallel to b up to 14.5 T. The intensity of the shoulder signal observed for H parallel to b has a maximum at similar to 6 T and vanishes above 10 T, although the superconductivity is confirmed by the chi(AC) measurements, which can survive up to 14.5 T (maximum H in the present measurement). Moreover, the decrease in K-b in the SC state starts to be small around 7 T and almost zero at 12.5 T. This indicates that the SC spin state gradually changes with the application of H. Meanwhile, in H parallel to c, an unexpected broadening without the shoulder signals was observed below T-c at 1 T, and this broadening was quickly suppressed with increasing H. We construct the H-T phase diagram for H parallel to b and H parallel to c based on the NMR measurements and discuss possible SC states with the theoretical consideration. We suggest that the inhomogeneous SC state characterized by the broadening of the NMR spectrum originates from the spin degrees of freedom.