Broad-band photometric colors and effective temperature calibrations for late-type giants. II. Z<0.02

(Abridged) We investigate the effects of metallicity on the broad-band photometric colors of late-type giants, and make a comparison of synthetic colors with observed photometric properties of late-type giants over a wide range of effective temperatures (T_eff=3500-4800 K) and gravities (log g=0.0-2.5), at [M/H]=-1.0 and -2.0. The influence of metallicity on the synthetic photometric colors is generally small at effective temperatures above \~3800 K, but the effects grow larger at lower T_eff, due to the changing efficiency of molecule formation which reduces molecular opacities at lower [M/H]. To make a detailed comparison of the synthetic and observed photometric colors of late type giants in the T_eff--color and color--color planes, we derive a set of new T_eff--log g--color relations based on synthetic photometric colors, at [M/H]=-0.5, -1.0, -1.5, and -2.0. While differences between the new T_eff--color relations and those available from the literature are typically well within ~100 K, effective temperatures predicted by the scales based on synthetic colors tend to be slightly higher than those resulting from the T_eff--color relations based on observations, with the offsets up to ~100 K. This is clearly seen both at [M/H]=-1.0 and -2.0, especially in the T_eff--(B-V) and T_eff--(V-K) planes. The consistency between T_eff--log g--color scales based on synthetic colors calculated with different stellar atmosphere codes is very good, with typical differences being well within \Delta T_eff~70 K at [M/H]=-1.0 and \Delta T_eff~40 K at [M/H]=-2.0.